# Maths- Percentages And Decimals

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## Reverse Percentages

A radio sells for £63, after a 40% increase in the cost price.

Solution

Start with the original amount as 100%.

Cost price = 100%

We are told the selling price is a 40% in the cost price.

So the selling price is 100% + 40% = 140% of the cost price.

We know that the selling price is £63, so 140% = £63.

Now calculate 1%:

140% = £63         1% = £63/140        1% = £0.45

The cost price is 100%, so multiply £0.45 by 100.

Cost price = 0.45 × 100 = £45.

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## Place value

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

• A tenth is 1/10 of a unit
• A hundredth is 1/100 of a unit
• A thousandth is 1/1000 of a unit

In the number 34.27, the value of the figure 2 is a tenth, and the value of the figure 7 is a hundredth

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## Ordering Decimals

When ordering numbers, we should always compare the digits on the left first.

For example, which is greater: 2.701 or 2.71?

## Example

Units       Tenths       Hundredths        Thousandths

2             7               0                       1

2             7              1                        0

Both numbers have two units and seven tenths, but 2.701 has no hundredths, whereas 2.71 has one hundredth. Therefore, 2.71 is greater than 2.701.

Another way to look at it is to write a zero at the end of 2.71 to make it 2.710 (this does not change its value, because it is after the decimal point).

The two numbers are now 2.710 and 2.701. It is quite easy to see that 2.710 is bigger (just as 2710 is bigger than 2701).

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## Adding and subtracting decimals

When adding and subtracting decimals add or subtract as normal, but make sure that you keep the decimal points aligned.

For example 4.27 + 2.3 =

•    4.27
• + 2.30
• ______
•    6.57

And to work out 5 - 0.24 we can write it:

•     5.00
• -   0.24
• ______
•     4.76

Note that we wrote 5 as 5.00. It is not essential to do this, but it helps.

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