Decimals

A simple meaning of the word ‘decimal’ is ‘connected with 10’. The decimal number system is a means of expressing any number from the largest to the smallest using the digits 0,1,2,3,4,5,6,7,8,9. To make all other numbers we use the same digits in different places in our decimal system.

Putting numbers into the place value chart.

These numbers are 241, 50062.5 and 0.013. The zero is called the ‘placeholder’ as it makes sure we realise the value of all other digits in the number.

This chart can be used to support multiplication and division by 10.

Decimal places

These are simply the series of numbers that comes after the decimal point.

For example,  0.02347661 is expressed to 8 decimal places as there are 8 digits after the decimal point.

Rounding up

The same rules as for significant figures apply:

a)      If the next number is 5 or more, we round up.

b)      If the next number is 4 or less, we do not round up.

Example

Express 7.8834 to 2 decimal places.

Since the number in the third decimal place is 3, we do not round up, giving the answer of 7.88.

Decimals and fractions

There is a direct link between decimals and fractions and decimals are often known as decimal fractions.

Example 1   If we put 0.4 into our place value chart, we see that 4 is in the 1/10 column.

So

    \dpi{100} 0.4 = \frac{4}{10}= \frac{2}{5}

Example 2   If we put 0.25 into our place value chart, we see that the 2 is in the 'tenth' (1/10) column and the 5 is in the 'hundredth' (1/100) column.

So     

     \dpi{100} 0.25 = \frac{2}{10}+\frac{5}{100}= \frac{25}{100}= \frac{1}{4}

 

To turn fractions into decimals we simply carry out division.

Example 3

\dpi{100} \frac{1}{2}= 1\div 2= 0.5

  

 
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