## Fractions and decimals

Decimal numbers are another way to represent numbers that are smaller than the unit 1. Decimals are written to the right of the units place separated by a period called **decimal point**. The first digit to the right of the decimal point represents tenths,
the second represents hundredths, the third represents thousandths, etc.

**If you want to compare or do calculations with fractions and decimals, you need to convert all of them to one type (either decimals or fractions).**

### Convert decimals to fractions:

**1. Convert the decimal to fraction** using tenths, hundredths, thousandths, etc. depending on the number of decimal places:

- one place=tenth, e.g. $0.5=5/10; ; 3.3=33/10$
- two places=hundredths, e.g. $0.02=2/100 ;; 0.12=12/100 ;; 1.38=138/100$
- three places=thousandth, e.g. $0.002=2/1000; ; 0.304=304/1000$

**2. Simplify the fraction to the lowest common term:**

### Convert fractions to decimals

**1. Find a number you can multiply by the denominator (bottom of the fraction) to make it 10, or 100, or 1000**, etc.

**2. A fraction in this form can be converted to a decimal**- just put the decimal point in the correct position (one space from the right hand side for every zero in the bottom number):

E.g. $5/10=0.5;$ ; $25/100=0.25$

For some numbers there is no way to multiply them to become tens, hundreds or thousands. For these numbers you can calculate an approximate decimal (finding a denominator close to 10, 100 or 1000):

### Convert whole numbers to fractions

Just put 1 below the whole number: