 Numbers, units and arithmetic

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# 1.6 Decimals and place value

What do the digits to the right of the decimal point mean? The first column to the right of the decimal point is obtained by dividing the units by 10; this is the ‘tenths’ column. Similarly the next column contains the hundredths, and so on. So here is the extended place value table: A tenth is 0.1 or 1 divided by 10, i.e. .

A hundredth is 0.01 or 1 divided by 100, i.e. .

A thousandth is 0.001 or 1 divided by 1000, i.e. .

So 0.101 is one tenth plus one thousandth or .

Notice that you need to include the zeros after the decimal point in numbers like 0.05 or 0.005, just as you do before the decimal point in numbers like 50 or 500, in order to indicate the place value of the 5. Also, note that often there is a 0 before the decimal point for numbers smaller than one. Whether it is written as 0.1 or .1 the value is still the same (one tenth). 0.1 is more usual when writing, .1 is more usual on calculators. In general, adding the zero before the decimal point is a clearer way of writing the number – the decimal point will then not be missed.

## Example 4

Two people go to a ‘pick your own’ orchard and gather a large bag of apples each. They weigh the bags and find the first weighs 6.85 kg and the second weighs 6.58 kg. Which is heavier?

The point at issue is which number is larger, 6.85 or 6.58. To determine this, write the digits in a place value table and then compare the values in each column: Again, work from the left. The digits in the units column are the same, so look at the next column. The first number has 8 tenths and the second number has 5 in this column (5 tenths), so the first number is bigger which means that the first bag is heavier.

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