# Decimals

A decimal number has a decimal point. The decimal point comes between the whole number part and the fractional part of the number. The whole number part is on the left of the decimal point and fractional part is on the right. The fractional part is made up of tenths, hundredths, thousandths etc.

Integers are positive and negative whole numbers and zero. So the decimal point comes at the end of the number as there are no fractional parts. The decimal point is usually not written but it is understood to be there if required. An integer number can be represented in decimal form, for example $5$ can be written as $5.00$.

##### Example 1

$17.382$

This number is greater than $17$ but not as large as $18$. In fact it is $17$ plus $3$ tenths plus $8$ hundredths plus $2$ thousandths. Or $\displaystyle{17+\frac{3}{10}+\frac{8}{100}+\frac{2}{1000}}$. As there are no further decimal values we say the decimal terminates.

##### Example 2

$0.33333\ldots$

This number is less than $1$ and the digit $3$ continues infinitely and is known as a recurring (repeating) decimal. This decimal can be written as $\displaystyle{\frac{3}{10}+\frac{3}{100}+\frac{3}{1000}+\frac{3}{10000}+\ldots}$ continuing forever. The neatest way to write the number is to put a dot over the digit that recurs, ie $0.\dot{3}$.

##### Example 3

$0.18181818\ldots$

This is also a recurring decimal and the best way to write the number is $0.\dot{1}\dot{8}$.

For each of the following numbers decide if they are terminating or recurring decimals.

 $6.759$ Terminating Recurring $4$ Terminating Recurring $-2.3$ Terminating Recurring $6.\dot{2}\dot{7}$ Terminating Recurring

#### Multiplying decimals by powers of ten

When you multiply a decimal number by 10, the result is a number which is ten times larger. Similarly when you multiply by 100, the result is 100 times larger than the original number.

##### Examples
• $6\times 10 = 60$
• $6.25 \times 100 = 625$

Complete the answers to the following questions.

 $18.56\times 10=$ $-120.98\times 100=$ $5.3\times 1000=$ $0.671\times 100=$ $-15\times 1000=$