# Decimals and fractions (medium)

2/5 = 0.4

## 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. 1 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, e.g. \$5/10=1/2 \;; 2/100 = 1/50\$.

### 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.
E.g.:

\$\$1/2={1×5}/{2×5}=5/10\$\$
\$\$1/4={1×25}/{4×25}=25/100\$\$

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), e.g.:

\$\$1/3={1×333}/{3×333}=333/999≅333/1000=0.333\$\$

### Convert whole numbers to fractions

Just put 1 below the whole number, e.g.:

\$\$8=8/1\$\$