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.

 

[show answer]


Question 2

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

 

[show answer]


Question 3

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

 

[show answer]


Question 4

Change 0.3 into a fraction.

 

[show answer]


Question 5

Change 0.65 into a fraction.

 

[show answer]


Question 6

Change 0.125 into a fraction.

 

[show answer]

 

 

 

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