- Convert between decimals and fractions
Write a Decimal as a Fraction
We often need to rewrite decimals as fractions or mixed numbers. Suppose you buy a sandwich and a bottle of water for lunch. If the sandwich costs [latex]\text{\$3.45}[/latex] , the bottle of water costs [latex]\text{\$1.25}[/latex] , and the total sales tax is [latex]\text{\$0.33}[/latex] , what is the total cost of your lunch?

The total is [latex]$5.03[/latex]. Suppose you pay with a [latex]$5[/latex] bill and [latex]3[/latex] pennies. Should you wait for change? No, [latex]\text{\$5}[/latex] and [latex]3[/latex] pennies is the same as [latex]\text{\$5.03}[/latex].
Because [latex]\text{100 pennies}=\text{\$1}[/latex], each penny is worth [latex]{\Large\frac{1}{100}}[/latex] of a dollar. We write the value of one penny as [latex]$0.01[/latex], since [latex]0.01={\Large\frac{1}{100}}[/latex].
Let’s see how we can convert decimal numbers to fractions. We know that [latex]$5.03[/latex] means [latex]5[/latex] dollars and [latex]3[/latex] cents. Since there are [latex]100[/latex] cents in one dollar, [latex]3[/latex] cents means [latex]{\Large\frac{3}{100}}[/latex] of a dollar, so [latex]0.03={\Large\frac{3}{100}}[/latex].
We convert decimals to fractions by identifying the place value of the farthest right digit. In the decimal [latex]0.03[/latex], the [latex]3[/latex] is in the hundredths place, so [latex]100[/latex] is the denominator of the fraction equivalent to [latex]0.03[/latex].
[latex]0.03={\Large\frac{3}{100}}[/latex]
For our [latex]$5.03[/latex] lunch, we can write the decimal [latex]5.03[/latex] as a mixed number.
[latex]5.03=5{\Large\frac{3}{100}}[/latex]
Notice that when the number to the left of the decimal is zero, we get a proper fraction. When the number to the left of the decimal is not zero, we get a mixed number.
How To: Convert a Decimal Number to a Fraction or Mixed Number
- Look at the number to the left of the decimal.
- If it is zero, the decimal converts to a proper fraction.
- If it is not zero, the decimal converts to a mixed number.
- Write the whole number.
- Determine the place value of the final digit.
- Write the fraction.
- numerator—the ‘numbers’ to the right of the decimal point
- denominator—the place value corresponding to the final digit
- Simplify the fraction, if possible.