DECIMALS AND PROPORTION

Multiplying, Dividing and Valuing Decimals

Multiplying, Dividing and Valuing Decimals

Valuing decimals

A decimal point is used to distinguish a part (tenths, hundredths etc.) from a whole number.

A tenth or 1/10 is 0.1 of a whole number

A hundredth or 1/100 is 0.01 of a whole number

A thousandth or 1/1000 is 0.001 of a whole number

For example

Units

Tenths

Hundredths

Thousandths

3 4 6 9
5 3 8 1
5 3 8 0

The above numbers would be written:

3.469

5.381

5.38

These numbers read from smallest to largest. 5.381 is 0.001 bigger than 5.38.

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Adding and subtracting decimals

Adding and subtracting decimals works the same way as whole numbers. You just need to make that the decimal point stays in the same position.

For instance:

5.68

+ 3.45

_______

9.13

If you have a whole number in the calculation it can help to make is a decimal by adding 0s to the end of it.

For example:

8.00

– 0.67

_______

7.33

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Multiplying or dividing decimals by multiples of 10 is relatively simple.

If you multiply by 10 the decimal point moves one space to the right:

35.8 x 10 = 358

If you multiply by 100 the decimal point moves two spaces to the right

35.8 x 100 = 3580

Notice that a zero is added. If there is no number to move onto then you need to add a zero. It might be easier to image the example number being written like this:

35.800000000…

Basically, the number of 0s indicates the number of spaces the decimal point should move to the right.

However, when you divide the decimal point moves to the left:

35.8 10 = 3.58

35.8 100 = 0.358

35.8 1000 = 0.0358

As you can see, there’s an infinite number of 0s going in the other direction too.

…0000000035.8

If you need to multiply a decimal number by another number then you just need to follow the same rules as with whole numbers.

mathsHowever, there are two points you should bear in mind: the number of digits after the decimal point in the question will equal the digits after the decimal point in the answer. So, if there’s a digit after the decimal point then the answer will also have a digit after the decimal point. Similarly with two digits and so on and so on.

For example:

6.78 x 3

First all remove the digit and calculate the answer as two whole numbers:

678

x 3

_______

2034

In the decimal in the question there were two digits after the decimal. So, following the rule above, there will be two digits after the decimal in the answer. So:

6.78 x 3 = 20.34

A good way to roughly check your answer is to round up each number to get as estimate:

7 x 3 = 21

If you need to divide a decimal by another number then you simply long divide as if you were using whole numbers. Note that you need to keep the decimal point in this time.

For example:

8.56 4

2.24

4