Decimals

Place value and ordering decimals

Decimal place values

We use a decimal point to separate units from parts of a whole (like tenths, hundredths, thousandths, etc).

0.1 is a tenth, 1/10 of a unit

0.01 is a hundredth, 1/100 of a unit

0.001 is a thousandth. 1/1000 of a unit

In 52.13, the value of the figure 1 is 1/10 , and the value of the figure 3 is 3/100.

Ordering decimals

When ordering numbers, always compare the left digits first.

Eg Which is greater, 2.301 or 2.32?

Units		Tenths	Hundredths	Thousandths
2	.	3	0	1
2	.	3	2

Both numbers have two units and three tenths, but 2.301 has no hundredths, whereas 2.32 has two hundredths. Therefore, 2.32 is greater than 2.301.

Adding a zero

Another way to look at it is to add a zero to the end of 2.32 (this doesn’t change its value as it’s after the decimal point).

The two numbers are now 2.320 and 2.301 and it is quite easy to see that 2.320 is bigger (just as 2 320 is bigger than 2 301).

Questions

Q1. In the number 3.546, what is the value of the figure 4?

Q2. Place the following numbers in order, smallest first: 3.2, 3.197, 3.02, 3.19

Adding and subtracting decimals

When adding and subtracting decimals, remember is to keep the decimal points in line in the question and the answer.

Adding decimals

Question

David is doing some DIY. He buys a 2m length of wood. He needs to cut two pieces of wood - one of length 0.6m and one of length 1.02m.

What is the total length of wood that David needs to cut?

Subtracting decimals

Question

David originally had 2m of wood. What is the length of the piece of wood that is left?

Multiplying decimals by 10, 100 and 1000

Multiplying by 10

When a decimal is multiplied by 10, every figure moves one place to the left.

What is 4.25 x 10? 42.5

Multiplying by 100

When multiplying by 100, every figure moves two places to the left.

Question

Which is bigger: 0.005 × 10 or 0.0004 × 1000?

Dividing decimals by 10, 100, 1000

Dividing by 10

When you divide by 10, every figure moves one place to the right. Hundreds become tens, tens become units, units become tenths and tenths become hundredths.

Dividing a decimal by 10

What is 27 divided by 10?

Dividing by 100

When you divide by 100, every figure moves two places to the right.

Dividing a decimal by 100

What is 27 divided by 100?

Dividing by 1000

When you divide by 1000, every figure moves three places to the right.

Dividing a decimal by 1000

What is 30 divided by 1000?

Multiplying a decimal by a whole number

Multiplying a decimal by a whole number is the same as multiplying two whole numbers. Remember:

If there is one digit after the decimal point in the question, there will be one digit after the decimal point in the answer.

If there are two digits after the decimal point in the question, there will be two digits after the decimal point in the answer.

Question

Calculate:

a) 2.43 × 7
b) 2.4 × 5
a) There were two digits after the decimal point in the question (4 and 3), so you must have two digits after the decimal point in the answer.

b) There was one digit after the decimal point in the question, so you must have one digit after the decimal point in the answer. The answer is therefore 12.0, but this can then be given as 12.

Check that you have a sensible answer by finding an approximate solution.

In the above example you were asked to calculate 2.4 × 5.

2 × 5 = 10, so you are looking for an answer which is slightly bigger than 10. So an answer of 12 seems sensible.

Dividing a decimal by a whole number

Remember to keep the decimal points aligned in the question and the answer.

Example

Work out 4.05 divided by 9

Solution:

Example

Work out 2.4 divided by 5

Solution:

It is sometimes necessary to add a ‘0′ or ‘0’s to the end of a decimal, as in this example (2.40 is the same as 2.4 but the question stays the same)

Multiplying by a number between 0 and 1

The multiplication sign can be replaced by ‘lots of’.

For example,

2 × 3 means 2 lots of 3
6 × 8 means 6 lots of 8

So, 1/2 × 10 means 1/2 of 10
And 1/3 × 12 means 1/3 of 12

When you multiply by a number greater than 1, you get an answer that is greater than the original number. But when you multiply by a number between 0 and 1, the answer is smaller than the original number.

In general:

m × 1/n = m ÷ n

Example

8 × 1/4 = 8 ÷ 4 = 2

20 × 1/5 = 20 ÷ 5 = 4

Dividing by a number between 0 and 1

Imagine that you had 10 bars of chocolate that you wanted to share amongst some children.

If you gave the children 2 bars each, you would have enough for 5 children.
10 ÷ 2 = 5

If you gave the children 1/2 bar each, you would have enough for 20 children.
10 ÷ 1/2 = 20

The pattern

Can you see what’s happening?

10 ÷ 2 = 5

10 ÷ 1/2 = 20

When you divide by a whole number the answer is less than the original number. When you divide by 1/2 the answer (20) is greater than the original number (10).

It’s the opposite of multiplying. When we divide by a number greater than 1, we get an answer that is less than the original number. But when we divide by a number between 0 and 1 the answer is larger than the original number.

So, 10 ÷ 1/2 = 20

Similarly, 10 ÷ 1/3 = 30 and 10 ÷ 1/4 = 40

In general:

m ÷ 1/n = mn

Questions

Q1. What is 10 ÷ 1/7 ?

Q2. Find the value of: 4 ÷ 1/3

BBC

TEST

Play games with decimals.