## Converting between fractions and decimals

Fraction to decimal (F -----> D)

There are common fractions whose decimal equivalents you might already know from everyday experience.

$\frac{1}{2}=0.5$

$\frac{1}{4}=0.25$ (A common name for $\frac{1}{4}$ is "one-quarter"...as in 25 cents.)

$\frac{3}{4}=0.75$

There are two ways to turn a fraction into a decimal:

• Method 1 - divide the numerator by the denominator
• Method 2 - rename the fraction so that the denominator is a power of 10 (ex. 10 or 100 or 1000, etc.)

Example 1:

 Convert $\frac{3}{5}$ into a decimal. Method 1: Division   (Not sure how to divide? Go here.) Method 2: Renaming

Example 2:

 Convert $\frac{11}{40}$ into a decimal. Method 1: Division Method 2: Renaming

### Decimal to fraction (D -----> F)

To turn a decimal into a fraction you need to be familiar with place value. Then reduce the fraction to its simiplest form.

 units tenths hundredths thousandths ten-thousandths 0 . 1 6 8 4

$0.1=\frac{1}{10}$

$0.16=\frac{16}{100}=\frac{8}{50}=\frac{4}{25}$

$0.168=\frac{168}{1000}=\frac{84}{500}=\frac{42}{250}=\frac{21}{125}$

$0.1684=\frac{1684}{10000}=\frac{842}{5000}=\frac{421}{2500}$

 Example 3: Convert 0.45 into a fraction.

 Example 4: Convert 0.0125 into a fraction.

# Self-Check

Question 1

Change $\frac{17}{20}$ into a decimal.

Question 2

Change $\frac{7}{8}$ into a decimal.

Question 3

Change $\frac{22}{40}$ into a decimal.

 Question 4 Change 0.3 into a fraction. [show answer]   $\large~\frac{3}{10}$

 Question 5 Change 0.65 into a fraction. [show answer]   $\large~\frac{13}{20}$

 Question 6 Change 0.125 into a fraction. [show answer]   $\large~\frac{1}{8}$