Writing Numbers in Expanded Form

example of writing the decimal 1.21 in expanded form

Writing a number in expanded form means to show the value of each non-zero digit in the number.

The number of non-zero digits tells us how many numbers will be shown in our expanded form answer.

Digits after the decimal point are worth less than one whole.

The 1 in the ones column is simply written as 1.

The 2 is in the tenths column and so, it is worth 2 out of 10.

2 tenths is written as a fraction as ² / ₁₀ .

The final 1 is in the hundredths column and so, it is worth 1 out of 100.

1 hundredth is written as a fraction as ¹ / ₁₀₀ .

The decimal 1.21 is written in expanded form as 1 + ² / ₁₀ + ¹ / ₁₀₀ .

Count the number of places that each digit is to the right of the decimal point to see how many zeros are in the fraction it is out of.

Writing a number in expanded form means to show the value of each digit in the number.

Each decimal digit is written as a fraction.

Decimals in Expanded Form example of 1.089

The digit of 1 before the decimal point is simply worth 1.

The digits to the right of the decimal point are written as fractions.

The number of places each digit is to the right of the decimal point is the number of zeros in the
denominatorThe number on the bottom of a fraction, below the line.
of the fraction.

We don’t write anything for the digit of 0.

The 8 is in the hundredths column, so we write it as ⁸ / ₁₀₀ .

8 is two places to the right of the decimal and so, 100 has two zeros.

The 9 is in the thousandths column and is written as ⁹ / ₁₀₀₀ .

The 9 is 3 places to the right of the decimal point and so, 1000 has 3 zeros.

1.089 is written in expanded form as 1 + ⁸ / ₁₀₀ + ⁹ / ₁₀₀₀ .

Supporting Lessons

Writing Numbers in Expanded Form Worksheets and Answers

Writing decimals in Expanded Form worksheet pdf

Comparing Number Sentences

Writing Decimals in Expanded Form

How to Write Decimals in Expanded Form

The expanded form of a number shows the value of each digit in the number. To write decimals in expanded form write the value of each digit with addition signs between them.

Digits to the left of the decimal point are whole numbers. Digits to the right of the decimal point are less than one and are written as fractions.

The number of places each digit is to the right of the decimal point is the same as the number of zeros in the

of the fraction.

For example, we will write the decimal number 5.1 in expanded form.

5 is in the one column and so is just worth 5.

The 1 is in the tenths column and so is worth 1 tenth.

Writing the decimal 5.1 in expanded form

1 tenth is written as ¹ / ₁₀ .

The digit at the top of the fraction is the digit we are looking at, which is 1.

The digit 1 is one place to the right of the decimal point and so the number on the bottom of the fraction contains 1 zero.

We can write the decimal 5.1 in expanded form as 5 + ¹ / ₁₀ .

Here is another example writing decimals in the expanded form. We will look at 2.3.

2 is in the ones column and so, it is just worth 2.

The 3 is in the tenths column and so, it is worth 3 tenths.

Writing decimals in expanded form example of 2.3

3 tenths is written as ³ / ₁₀ .

The digit on the top of the fraction is the digit we are looking at, which is 3. This digit is one place right of the decimal point and so, the number on the bottom of the fraction contains one zero.

The decimal number 2.3 is written in expanded form as 2 + ³ / ₁₀ .

The next example is 1.21. We will write this decimal in expanded form.

1 is in the ones column and so, it is just worth 1.

The 2 is in the tenths column and so, it is written as ² / ₁₀ .

The final 1 is in the hundredths column and so, it is worth 1 hundredth.

Writing the decimal 1.21 in expanded form

1 hundredth is written as ¹ / ₁₀₀ .

The digit on the top of the fraction is the digit we are looking at, which is 1. This digit is two places to the right of the decimal point and so the number on the bottom of the fraction contains two zeros.

The decimal 1.21 is written in expanded form as 1 + ² / ₁₀ + ¹ / ₁₀₀ .

The next example of writing decimals in expanded form is 0.37.

Remember that we only write the values of non-zero digits. We ignore the 0 in the ones column because it is not worth anything.

The 3 is in the tenths column and so it is worth 3 tenths, ³ / ₁₀ .

The 7 is in the hundredths column and so it is worth 7 hundredths, ⁷ / ₁₀₀ .

example of writing the decimal 0.37 in expanded form

We can write 0.37 in expanded form as ³ / ₁₀ + ⁷ / ₁₀₀ .

Notice that we only have two non-zero digits in 0.37: 3 and 7. Therefore we only have two numbers in our expanded form answer.

Here is our next example of writing 4.231 in expanded form.

4 is in the ones column and is worth 4.

2 is in the tenths column and is worth 2 tenths, ² / ₁₀ .

3 is in the hundredths column and is worth 3 hundredths, ³ / ₁₀₀ .

The 1 is in the thousandths column and is worth 1 thousandth, ¹ / ₁₀₀₀ .

Writing decimals in expanded form example of 4.231

The 1 is three places to the right of the decimal point and so the fraction ¹ / ₁₀₀₀ contains 3 zeros on the bottom.

The decimal number 4.231 is written in expanded form as 4 + ² / ₁₀ + ³ / ₁₀₀ + ¹ / ₁₀₀₀ .

In the next example we write 0.503 in expanded form.

We only consider the digits that are not zero.

We have 5 tenths, which is written as ⁵ / ₁₀ .

We have 3 thousandths, which is written as ³ / ₁₀₀₀ .

Expanded form of the decimal 0.503

0.503 is written in expanded form as ⁵ / ₁₀ + ³ / ₁₀₀₀ .

In the next example we write the decimal 1.089 in expanded form.

The 1 is in the ones column and is simply written as 1.

We ignore the zero.

The 8 is in the hundredths column and is written as ⁸ / ₁₀₀ .

The 9 is in the thousandths column and is written as ⁹ / ₁₀₀₀ .

Writing decimals in expanded form with thousandths example

1.089 is written in expanded form as 1 + ⁸ / ₁₀₀ + ⁹ / ₁₀₀₀ .

There are 3 non-zero digits in 1.089: 1, 8 and 9.

This means our expanded form answer is made up of three numbers added together.

Now try our lesson on Comparing Number Sentences where we learn how to use <, > and = signs in number sentences.

less-than-greater-than

Protected: Mathematics Assessment

Writing Numbers in Expanded Form

example of writing numbers in expanded form. 149 in expanded form

Writing a number in expanded form means to show the value of each digit in the number.

We start in the ones column.

9 is simply 9 ones so we just write 9.

4 is in the tens column so is worth 40.

1 is in the hundreds column so is worth 100.

We write 149 in expanded form as 100 + 40 + 9.

We write the values as a sum.

Writing a number in expanded form means to show the value of each digit in the number.

We write each of these values added together.

Example of writing a number in expanded form 79020

To write 79020 in expanded form we show the value of each digit in the number.

Because the digit of 0 is not worth anything, we do not write it.

The next smallest digit after zero is 2.

2 is in the tens column and is worth 20.

The next digit in the hundreds column is 0 and so, we do not write it.

The next digit in the thousands column is 9, which is worth 9000.

Finally, we have a 7 in the ten-thousands column, which is worth 70000.

79020 is written in expanded form as 70000 + 9000 + 20

Supporting Lessons

Writing Numbers in Expanded Form Worksheets and Answers

Writing Numbers in Expanded Form worksheet pdf

What are Odd and Even Numbers?

Writing Numbers in Expanded Form

What is Expanded Form

Writing a number in expanded form means to write the value of each digit in the number. The number is written as the sum of the separate place values of each digit.

For example 70 is written in expanded form as 70 + 2.

example of writing 72 in expanded form as 70 + 2

72 is made of two digits: 7 and 2.

The 7 is in the tens column and is worth 70. The 2 is in the ones column and is worth 2.

How to Write a Number in Expanded Form

To write a number in expanded form write the value of each non-zero digit in the number with addition signs between them.

The amount of numbers added together in the expanded form answer will be the same of the amount of non-zero digits in the original number.

Here is an example of writing the number 149 in expanded form.

We have 3 non-zero digits, which are 1, 4 and 9. This means that our expanded form answer will be made up of three numbers added together.

writing 149 in expanded form

The value of each digit is equal to the digit multiplied by the value of the place value column it is in.

The 9 is in the ones column and 9 × 1 = 9. We just write 9.

The 4 is in the tens column and 4 × 10 = 40. The 4 is worth 40.

The 1 is in the hundreds column and 1 × 100 = 100. Therefore this 1 is worth 100.

149 is written in expanded form as 100 + 40 + 9.

The values of the digits are written in the same order as the original number and they all have addition signs between them.

For whole numbers, we can also see that the value of each digit is the same as taking the digit and replacing the digits to the right of it in the number with a zero.

For example, to find the value of the digit 1 in 149, replace the 4 and the 9 with zeros. The digit 1 in 149 is worth 100.

In this next example we will write the number 603 in expanded form.

We don’t include any zeros in our number when writing it in expanded form.

The number 603 is made up of just two non-zero digits: 6 and 3.

This means that when we write 603 expanded form it is made up of two numbers added together.

Writing the number 603 in expanded form

The digit 3 is in the ones column and so is just worth 3.

The 0 is not worth anything so we do not write it.

The 6 is in the hundreds column and so it is worth 6 hundred. We can also see this by replacing the digits to the right of 6 in 603 with zeros. The 6 is worth 600.

We write 603 in expanded form as 600 + 3.

In this next example we will write 3255 in expanded form.

3255 is made up of 4 non-zero digits: 3, 2, 5 and 5.

This means that when we write it in expanded form it will be written as the sum of 4 different numbers.

how to write the number 3255 in expanded form

Starting with the digits on the right, the 5 is in the ones column and is worth 5.

The next 5 is in the tens column and is worth 50.

The 2 is in the hundreds column and is worth 200.

Finally, the 3 is in the thousands column and is worth 3000.

3255 is written in expanded form as 3000 + 200 + 50 + 5.

In this next example we will write 24718 in expanded form.

There are 5 non-zero digits so the answer will be made up of 5 different numbers.

24718 in expanded form

The 8 is in the ones column and is worth 8.

The 1 is in the tens column and is worth 10.

The 7 is in the hundreds column and is worth 700.

The 4 is in the thousands column and is worth 4000.

The 2 is in the ten-thousands column and is worth 20000.

24718 is written in expanded form as 20000 + 4000 + 700 + 10 + 8.

In this example we write 79020 in expanded form.

Remember that we do not write zeros in expanded form.

We have 3 non-zero digits: 7, 9 and 2.

This means that the answer will be made up of 3 numbers added together.

Expanded Form of the number 79020

The 2 is in the tens column and is worth 20.

The 9 is in the thousands column and is worth 9000.

The 7 is in the ten-thousands column and is worth 70000.

The number 79020 is written in expanded form as 70000 + 9000 + 20.

Now try our lesson on What are Odd ad Even Numbers where we learn about odd and even numbers.

odd and even numbers

Rounding to Significant Figures

Counting the significant figures of the decimal number 0.04013

To round the decimal number 0.04013 to 3 significant figures we first need to count the number of significant figures that it has.

We start counting significant figures from the first number that is not zero.

The first two digits of 0.04013 are zeros, so we ignore them.

The first significant digit is 4 because it is the first digit that is not zero.

So 4 is the first significant figure, 0 is the 2nd, 1 is the 3rd and 3 is the 4th.

We have 4 significant figures.

Notice that we count the zero after the 4 because we have started counting at 4.

Example of rounding the decimal number 0.04013 to 3 significant figures

We draw a line after the significant figure that we are rounding to.

We are rounding to 3 significant figures so we draw a line after the 3rd significant figure of 1.

We look at the digit after the line to decide whether to round up or down.

If it is 5 or more, we round up and if it is 4 or less we round down.

3 is 4 or less and so we round down.

This means that we leave the 1 before the line as a 1.

The digit after the line becomes a zero.

We do not write zeros on the end of decimals and so, we remove it.

0.04013 rounded to 3 significant figures is 0.0401.

Count significant figures from the first non-zero digit.

If the next digit is 5 or more, round up or if it is 4 or less, round down.

Counting the significant figures of 549

We count significant figures from the first digit that is not zero.

The first digit is 5, which is not zero and so, we start counting.

5 is the first significant figure, 4 is the 2nd and 9 is the 3rd.

549 has 3 significant figures.

Rounding the whole number 549 to 2 significant figures

We are rounding 549 to 2 significant figures, so we draw a line after the second significant figure of 4.

We look at the number after the line to decide whether to round up or down.

If this number is 5 or more, we round up and if it is 4 or less, we round down.

9 is 5 or more and so we round up.

To round up we increase the number before the line by 1 and change the number after the line to a 0.

549 rounds up to 550 when written to 2 significant figures.

Supporting Lessons

Rounding to Significant Figures Worksheets and Answers

Rounding to significant figures worksheet pdf

Rounding to significant figures worksheet answers pdf

Converting Decimals to Fractions

How to Round a Number to Significant Figures

Rules for Rounding Off Significant Figures

Rounding means to simplify a number by writing it to a number that it is close to.

To round a number off to significant figures use these steps:

Read the digits of the number from left to right.
Start counting the digits from the first digit that is not zero.
Count the digits until you get to the significant figures required.
Draw a line after this number.
If the number after the line is 5 or more, round up or if it is 4 or less, round down.
To round up, add 1 to the number before the line and change the numbers after the line to 0.
To round down, keep the number before the line the same and change the numbers after the line to 0.

We will look at some examples of rounding numbers to significant figures.

Rounding a Whole Number to Significant Figures

To round a whole number to a given significant figure, look at the digit after the significant figure required. If this digit is 5 or more, round up or if it is 4 or less, round down.

To round a whole number up, increase the significant figure required by 1 and change the digits that follow it to zero.

To round a whole number down, keep the significant figure required as it is and change the digits that follow it to zero.

In this example, we have 549.

Reading from left to right, the first digit is 5, which is not 0. So we start counting.

example of counting the number of significant figures in 549

5 is the first significant figure.

4 is the second significant figure.

9 is the third significant figure.

549 has 3 significant figures.

We will now round 549 to 2 significant figures.

Since we are rounding to 2 significant figures, we draw a line after the 2nd significant figure.

We draw a line after the 4 and look at the number after this line to decide whether to round up or down.

Rounding 549 to 2 significant figures

If the number is 5 or more, we round up or if the number is 4 or less, we round down.

9 is 5 or more and so, we round up.

To round up, we increase the number before the line by 1 and change the numbers after the line to zeros.

4 becomes 5 and the 9 becomes a zero.

549 rounds up to 550 when rounded to 2 significant figures.

The 2nd significant figure of this number is in the tens column and so we are deciding between rounding to 540 or 550.

Rounding means to write down the number that is closest.

We can see that 549 is one away from 550 on the number line below but 9 away from 540.

Rounding 549 to 550

549 is nearer to 550 than it is to 540.

We will now round 549 to 1 significant figure.

The first significant digit is the 5 in the hundreds column. This means we have a choice of rounding 549 to 500 or to 600.

The first significant figure in 549 is the 5. We draw the line after this digit.

We look at the digit after the line to decide whether to round up or down.

Rounding to 549 to 1 significant figure

The digit after the line is a 4. It is 4 or less and so we round down.

To round 549 down, we keep the number before the line the same and change the numbers after the line into zeros.

549 rounds down to 500 when written to 1 significant figure.

This means that 549 is nearer to 500 than it is to 600.

Because all whole numbers begin with a non-zero digit, a whole number has the same number of significant figures as it has digits. All of its digits are significant.

Simply count the digits in a whole number to see how many significant digits it has.

Rounding Decimal Numbers to Significant Figures

To round a decimal to a given number of significant figures, look at the digit after the significant figure required. If it is 5 or more, the number rounds up or if it is 4 or less, the number rounds down.

To round a decimal up, the significant figure increases by 1 and the rest of the digits that follow this digit are removed.

To round a decimal down, the significant figure remains the same and the rest of the digits that follow this digit are removed.

When rounding decimals to significant figures it is important to remember that zeros at the beginning of the number are not significant digits.

We only start counting significant figures from the first digit that is not zero.

In this first example we have 0.0471.

This number has two zero digits at the front, which we do not count.

Counting the significant figures in 0.0471

The 4 is the first digit that is not zero and so, we start counting at 4.

4 is the first significant figure.

7 is the second significant figure.

1 is the third significant figure.

We will now round 0.0471 to 1 significant figures.

The first significant figure is the 4 in the hundredths column. We have the choice of keeping the 4 as 4 or rounding it up to a 5.

The choice is to round down to 0.04 or round up to 0.05.

We draw a line after the 4 and look at the next digit after the line to decide how to round off this number.

Rounding the decimal 0.0471 to 1 significant figure

The next digit is a 7 and it is 5 or more. We round up.

To round up, the 4 becomes a 5 and the digits after the line become zero.

0.0471 is nearer to 0.0500 than it is to 0.04,

0.0471 rounds up to 0.0500. However we do not write zeros at the end of a decimal number and instead we write 0.0500 as 0.05.

0.0471 rounds up to 0.05.

In this next example of rounding a decimal to significant figures we have 0.25.

Remember that we do not start counting the digits until we have a digit that is not zero.

We ignore the 0 at the start of 0.25 and start counting at the 2.

Counting the significant figures in 0.25

2 is the first significant figure.

5 is the second significant figure.

We will now round 0.25 to 1 significant figure.

2 is our first significant figure and so we draw our line after it.

Rounding 0.25 to 1 significant figure

We look at the next digit along to decide whether to round up or down.

The next digit is a 5.

5 is included in ‘5 or more’ and so we round up.

We increase the 2 to a 3 and the digits after the line are changed to 0.

0.25 rounds up to 0.30. However we do not write zeros at the end of a decimal number. We write 0.30 as 0.3.

We say that 0.25 rounds up to 0.3.

0.25 is exactly half way between 0.2 and 0.3. We choose to round up numbers that end in the digit 5.

This is because if any other digit came after the 5, the number would round up.

In this example, 0.259 would round up, 0.251 would round up and even 0.250001 would round up. All of these numbers are nearer to 0.3 than 0.2. We include 0.25 so that we have a consistent rule for rounding.

In this next example we have 0.04013.

We have 2 zeros at the beginning of this decimal number and so we do not count these as significant figures.

The first non-zero digit is the 4.

Counting the significant figures in the decimal number 0.04013

4 is the first significant figure.

0 is the second significant figure. We count this zero because we have started counting the significant figures with 4. This 0 comes after a non-zero digit so it is counted.

1 is the third significant figure.

3 is the fourth significant figure.

We will now round the decimal 0.04013 to 3 significant figures.

1 is our third significant figure and so we draw our line after the 1.

We look at the next digit along, after the line, to decide whether to round up or down.

Rounding the decimal number 0.04013 to 3 significant figures

The digit after the line is a 3. It is 4 or less and so we round down.

The 1 remains as a 1 and the digits after the line are removed.

The decimal number 0.04013 is rounded down to 0.0401 when written to 3 significant figures.

Examples of Rounding to Significant Figures

This table contains some examples of rounding different numbers to 1, 2 or 3 significant figures.

Number	1 Significant Figure	2 Significant Figures	3 Significant Figures
8158	8000	8200	8160
6.711	7	6.7	6.71
0.67351	0.7	0.67	0.674
0.03094	0.03	0.031	0.0309
2.103411	2	2.1	2.10

8158 is rounded down to 8000 when written to 1 significant figure. This is because the 1 is ‘4 or less’.

8158 is rounded up to 8200 when written to 2 significant figures. This is because the 5 is ‘5 or more’ and rounds 1 up to 2.

8158 is rounded up to 8160 when written to 3 significant figures. This is because 8 is ‘5 or more’ and rounds the 5 up to a 6.

6.711 rounds up to 7 when written to 1 significant figure. This is because the 7 is ‘5 or more’ and rounds 6 up to 7.

6.711 rounds down to 6.7 when written to 2 significant figures. This is because the first 1 is ‘4 or less’.

6.711 rounds down to 6.71 when written to 3 significant figures because the second 1 is ‘4 or less’.

0.67351 rounds up to 0.7 when written to 1 significant figure because the 7 is ‘5 or more’ and rounds the 6 up to a 7.

0.67351 rounds down to 0.67 when written to 2 significant figures because the 3 is ‘4 or less’.

0.67351 rounds up to 0.674 when written to 3 significant figures because the 5 is ‘5 or more’ and rounds the 3 up to a 4.

0.03094 rounds down to 0.03 when written to 1 significant figure because the 0 after the 3 is ‘4 or less’.

0.03094 rounds up to 0.031 when written to 2 significant figures because the 9 is ‘5 or more’ and rounds the 0 up to a 1.

0.03094 rounds down to 0.0309 when written to 3 significant figures because the 4 is ‘4 or less’.

2.103411 rounds down to 2 when written to 1 significant figure because the 1 is ‘4 or less’.

2.103411 rounds down to 2.1 when written to 2 significant figures because the 0 is ‘4 or less’.

2.103411 rounds down to 2.10 when written to 3 significant figures because the 3 is ‘4 or less’. We can write this number as 2.1 or 2.10 but we will write 2.10 because the question asks for 3 significant figures.

Now try our lesson on Converting Decimals to Fractions where we learn how to write decimals as fractions.

$converting decimals to fractions$

Reading Timetables

The time that each bus leaves each location is written alongside it in the same row.

Each column shows the journey of a different bus.

We can read the journey of each bus by reading downwards.

The Market is the first stop and the School is the last stop.

Later times are shown to the right.

Reading a bus timetable example

The 12:42 bus from the hospital is in the same row as the hospital

We read across from the word hospital until we see 12:42.

We mark this bus as the bus we will catch.

We read downwards to see where it goes next.

The School is the next stop and it gets there at 13:11.

Each bus travels downwards down each column of the timetable.

Each time shows when the bus arrives at the location listed in the same row to the left.

Reading Timetables example of a journey

Bus B leaves the hospital at 10:48.

Bus B gets to the school at 11:10.

To work out the duration of the journey we find the difference between 11:10 and 10:48.

The hours are different and so we can count from 10:48 to 11:00 and then from 11:00 to 11:10.

There are 60 minutes in an hour and the time from 10:48 to 11:00 is 60 – 48, which is 12 minutes.

We then have a further 10 minutes from 11:00 to 11:10.

The journey takes a total of 22 minutes

Supporting Lessons

Reading Timetables Worksheets and Answers

reading timetables worksheet answers pdf

Reading and Interpreting Timetables

How to Read a Bus Timetable

To read a bus timetable, look down the left column to find the name of the station you are at. The times that each bus leaves this station are in the same row to the right. Now read downwards from a chosen time to see what time this bus reaches the coming destinations.

A bus timetable is written in columns. Each new bus journey is written in its own column.

Below is an example of a bus timetable being created.

We have four different buses: Bus A, Bus B, Bus C and Bus D, which are each in their own column.

how to read a bus timetable

We can see Bus A’s journey begins at the market at 08:00.

Its next stop is at the cinema. It leaves the cinema at 08:10.

Then the bus goes to the hospital. It leaves the hospital at 08:25.

The final stop is at the school. It arrives at the school at 08:47.

When reading a timetable, the time shown is the time that we leave that location. It is possible for the bus or train to arrive earlier than this time but if it does, it should wait at this location until the time written on the timetable.

The only case where this is not true is in the final location, where the time shown is the time that the bus or train arrives at this stop.

bus timetable

We can see that Bus B leaves the market at 10:20, leaves the cinema at 10:32, leaves the hospital at 10:48 and arrives at the school at 11:10.

Bus C leaves the market at 12:20, leaves the cinema at 12:26, leaves the Hospital at 12:42 and arrives at the School at 13:11.

Bus D leaves the market at 16:55, leaves the cinema at 17:10, leaves the hospital at 17:33 and arrives at the school at 18:01.

Here is an example of reading a bus timetable.

“I catch the 12:42 bus from the hospital. When do I arrive at school?”

We first find the hospital station in the left column and read across from this row to find the bus that leaves at 12:42.

Reading a bus timetable to find the time of arrival

We now read downwards to see the rest of the journey after it leaves the hospital. After the hospital stop, the bus arrives at the school. The bus arrives at school at 13:11.

In this next example, “I am at the cinema and it is 11:50. When is the next bus?”

We need to read the times of the different buses that leave the cinema. We read from the same row as the cinema.

The times of buses that leave the cinema are: 08:10, 10:32, 12:26 and 17:10.

Reading bus schedules to find the next bus

It is 11:50, so I have already missed the 08:10 and 10:32 buses. The next bus is at 12:26.

In this next example we are asked, “How long does it take Bus A to get from the market to the cinema?”

We need to find the time when Bus A leaves the market and the time it arrives at the cinema. We then find the difference between these times.

Reading a bus schedule to find how long a bus journey takes

Reading the schedule, Bus A leaves the market at 08:00 and arrives at the cinema at 08:10.

We now find the difference between these times. The hours are the same as they are both 8 o’clock. We can see that from 08:00 to 08:10, the bus has taken 10 minutes.

In this next example we are asked, “How long does it take Bus A to get from the hospital to the school?”

Reading the bus schedule, we can see that Bus A leaves the hospital at 08:25 and arrives at the school at 08:47.

Reading a bus schedule to see how long a journey takes

Again both times have the same hour of 8 o’clock. So to find the difference between the times, we simply find the difference between the minutes.

To find the difference, we subtract.

47 – 25 = 22 and so, the journey takes 22 minutes.

In this next example we are asked, “How long does it take Bus B to get from the hospital to the school?”

Bus B leaves the hospital at 10:48 and arrives at the school at 11:10.

This time the hour times are different. One is after 10 o’clock and the next time is after 11 o’clock.

example of reading a bus timetable

Because the hours are different, we find the minutes to the next hour and count on from there.

We first find the time from 10:48 until the next hour, 11 o’clock.

There are 60 minutes in an hour so the time taken from 10:48 to the next hour is 60 – 48.

60 – 48 = 12, so the time to 11:00 is 12 minutes.

We now count on from 11:00 to 11:10. This is an extra 10 minutes.

In total, the time taken is 12 minutes plus 10 minutes.

The journey takes a total of 22 minutes.

We are now asked, “How long does it take Bus D to get from the market to the hospital?”

Bus D leaves the market at 16:55. It arrives at the hospital at 17:33.

example of reading a bus schedule

Again the hours are different and so, we count on from 16:55 to 17:00 before counting on to 17:33.

16:55 is five to 17:00 and so it is 5 minutes until 17:00.

We then have a further 33 minutes until 17:33.

In total we have 5 minutes plus 33 minutes. The journey took 38 minutes.

In these examples, we will look at examples of reading a bus timetable with buses running from Worcester to Rubery.

A bus timetable example

We can see that not all stops have times written next to them. This means that the bus does not stop at this station.

If there is no time written for a station then the bus will skip this station and go directly to the next one down on the schedule with a time next to it.

In this example we have, “I catch the 07:16 bus from Fernhill. Will I be able to get off in Sidemoor?”

We first find the 07:16 bus that is in line with the Fernhill stop. We then read downwards until we find the box in line with the Sidemoor stop.

Reading a bus timetable where buses don't stop at every station

We can see that after the bus leaves Fernhill at 07:16, it leaves Droitwich at 07:29. There is no time next to the Wychbold station and then there is no time next to the Sidemoor station.

This means that this bus does not stop at either of these two stations. I will not be able to get off the bus in Sidemoor.

In this next example of reading a bus timetable, “It is 06:30 and I am in Wychbold. When is the next bus?”

We can read across the row from Wychbold to see what times the bus leaves this station.

Reading a bus timetable from worcester

A bus leaves Wychbold at 05:55, then the next bus does not arrive at Wychbold, then a bus leaves Wychbold leaves at 08:25. The final bus also does not stop at Wychbold.

If it is 06:30, then I have missed the 05:55 bus. The next bus that stops here is at 08:25.

I can catch the 08:25 bus.

In the next example, “It is 06:55 and I am in Worcester. When will I get to Catshill?”

Example of reading a bus timetable from worcester to catshill

We can see that I have missed the 05:30 bus and the next bus is at 07:05.

We can read down from 07:05 to see what time this bus arrives in Catshill.

We leave Fernhill at 07:16, we don’t stop at Wychbold or Sidemoor and then leave Catshill at 08:00.

We know that we must be in Catshill at 08:00.

In this next example, “I catch the 07:50 bus from Worcester. How long will it take to get to Rubery?”

We leave Worcester at 07:50 and get to Rubery at 09:02.

working out travel times using a bus timetable

We can see that the hours are different so we count from 07:50 to 08:00, then from 08:00 to 09:00 and finally from 09:00 to 09:02.

There are 60 minutes in an hour so the time from 07:50 to 08:00 is 60 – 50.

This is 10 minutes.

We then have an hour from 08:00 to 09:00. This is 1 hour 10 minutes so far in total.

We then have another 2 minutes from 09:00 to 09:02. This is 1 hour 12 minutes in total.

This journey takes 1 hour 12 minutes.

Reading Timetables with a Circular Route

Here is an example of a timetable with a loop.

We have just one bus that travels from the City to the Museum to the Beach to the Cathedral and then back to the City to complete another circuit.

Reading a bus timetable with a loop

The bus leaves the city at 11:30 and gets back to the city at 13:21.

The bus then waits in the city breifly.

We can see in the next column along that this bus then leaves the city again at 13:30. It gets back to the city again at 15:32.

It waits at the city again before leaving.

We can see in the next column along that this bus leaves the city at 15:40 and returns to the city at the end of the day at 17:30. It does not leave the city again.

In this example we are asked, “I am at the beach and need to get to the city. What is the latest bus I can catch?”

We first need to find at which times the bus leaves the beach.

We read the schedule and see that buses leave the beach at 12:38 and 14:42. There is no bus after this that stops at the beach. The final bus does not stop at the beach. We know this because there is no time in this row after 14:42.

Reading a bus timetable

In this next example we are asked, “I get on the 13:04 bus at the cathedral. What time will I get to the museum?”

We find the 13:04 bus that leave the cathedral and follow its path down.

Reading bus timetables that run in a circuit loop

After leaving the cathedral at 13:04, the bus arrives at the city at 13:21. The bus waits at the city before leaving at 13:30. We can see this at the top of the next column along.

It then gets to the museum at 13:52.

In this example we are asked, “It is 15:28 and I am in the city. How long will it take the next bus to get to the museum?”

The next bus arrives at the city at 15:32. It leaves the city at 15:40.

It gets to the museum at 16:02.

Reading Timetables of a bus operating in a loop route

The bus journey begins at 15:40 and ends at 16:02.

The hours are different and so to work out the duration, we count from 15:40 to 16:00 and then from 16:00 to 16:02.

There are 60 minutes in an hour so from 15:40 to 16:00 it is 60 – 40 minutes. This is 20 minutes so far.

We then have 2 more minutes from 16:00 to 16:02.

In total we have 22 minutes.

Now try our lesson on Repeating Shape Patterns where we learn how to find missing shapes in different patterns.

Roman Numerals 1 to 10

roman numerals to 10

Finding Prime Numbers to 100

prime numbers to 100 displayed on a grid

The grid above shows the prime numbers to 100.

Prime numbers cannot be made by multiplying other smaller whole numbers.

Prime numbers can only be written as 1 × themselves.

We say that a prime number has exactly 2 factors, which are the number 1 and the number itself.

Apart from 2 and 5, the other prime numbers only end in a 1, 3, 7 or 9.

A number is not prime if it is in the times table of another number.

The prime numbers to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.

list of prime numbers to 100

Prime numbers cannot be made by multiplying 2 other smaller whole numbers.

Apart from 2 and 5, prime numbers only end in a 1, 3, 7 or 9.

Identifying Prime Numbers 3

7 is an example of a prime number.

7 cannot be made by multiplying two smaller whole numbers together.

7 can only be written as 1 × 7.

We cannot divide any other whole number into 7 exactly.

We can try dividing by 2, 3, 4, 5 or 6 and see that these numbers do not go into 7 exactly.

Supporting Lessons

Prime Numbers to 100 Worksheets and Answers