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Study Guides > Mathematics for the Liberal Arts Corequisite

Converting Decimals to Fractions or Mixed Numbers

Learning Outcomes

  • Convert a decimal to a fraction or mixed number

We often need to rewrite decimals as fractions or mixed numbers. Let’s go back to our lunch order to see how we can convert decimal numbers to fractions. We know that $5.03 means 55 dollars and 33 cents. Since there are 100100 cents in one dollar, 33 cents means 3100{\Large\frac{3}{100}} of a dollar, so 0.03=31000.03={\Large\frac{3}{100}}.

We convert decimals to fractions by identifying the place value of the farthest right digit. In the decimal 0.030.03, the 33 is in the hundredths place, so 100100 is the denominator of the fraction equivalent to 0.030.03.

0.03=31000.03={\Large\frac{3}{100}}

For our $5.03 lunch, we can write the decimal 5.035.03 as a mixed number.

5.03=531005.03=5{\Large\frac{3}{100}}

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.

Convert a decimal number to a fraction or mixed number.

  1. 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.
  2. Determine the place value of the final digit.
  3. Write the fraction.
    • numerator—the ‘numbers’ to the right of the decimal point
    • denominator—the place value corresponding to the final digit
  4. Simplify the fraction, if possible.
 

example

Write each of the following decimal numbers as a fraction or a mixed number:
  1. 4.094.09
  2. 3.73.7
  3. 0.286-0.286
Solution:
1.
4.094.09
There is a 44 to the left of the decimal point. Write "44" as the whole number part of the mixed number. .
Determine the place value of the final digit. .
Write the fraction. Write 99 in the numerator as it is the number to the right of the decimal point. .
Write 100100 in the denominator as the place value of the final digit, 99, is hundredth. 491004{\Large\frac{9}{100}}
The fraction is in simplest form. So, 4.09=491004.09=4{\Large\frac{9}{100}}
Did you notice that the number of zeros in the denominator is the same as the number of decimal places?
2.
3.73.7
There is a 33 to the left of the decimal point. Write "33" as the whole number part of the mixed number. .
Determine the place value of the final digit. .
Write the fraction. Write 77 in the numerator as it is the number to the right of the decimal point. .
Write 1010 in the denominator as the place value of the final digit, 77, is tenths. 37103{\Large\frac{7}{10}}
The fraction is in simplest form. So, 3.7=37103.7=3{\Large\frac{7}{10}}
3.
0.286−0.286
There is a 00 to the left of the decimal point. Write a negative sign before the fraction. .
Determine the place value of the final digit and write it in the denominator. .
Write the fraction. Write 286286 in the numerator as it is the number to the right of the decimal point. Write 1,0001,000 in the denominator as the place value of the final digit, 66, is thousandths. 2861000-{\Large\frac{286}{1000}}
We remove a common factor of 22 to simplify the fraction. 143500-{\Large\frac{143}{500}}
 

try it

[ohm_question]146573[/ohm_question] [ohm_question]146574[/ohm_question] [ohm_question]146575[/ohm_question]

In the next video example, we who how to convert a decimal into a fraction.

https://youtu.be/0yYQLZcTEXc

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