Last modified on August 3rd, 2023

chapter outline


Decimal to Mixed Number

Most of the decimals can be converted to mixed numbers, except some numbers that are irrational. Here we will talk about how to convert a decimal to a mixed number easily. We can do the conversion with a calculator. However, it is crucial for us to understand the concept.

How to Convert Decimal to Mixed Numbers

Decimal to Mixed Number
  1. Notice the number of digits after the decimal place. Separate the digits before and after the decimal point and write them in an addition sentence. (E.g., 3.64 = 3 + .64)
  2. Remove the decimal point from the second part (write .64 as 64). Divide the number by a 10n, where n = number of decimal places. So, if there are two digits after the decimal point, divide number by 100. If there are three digits after the decimal point, divide number by 1000. In other way, the number of zeros must equal the number of decimal places. (.64 = 64/100)
  3. Reduce the fraction. Add this reduced fraction with the whole number. (${\dfrac{64}{100}=\dfrac{16}{25}}$, so the final mixed number is 3 + ${\dfrac{16}{25}}$ ${=3\dfrac{16}{25}}$

We can easily determine whether a decimal is a proper or improper fraction. If it is greater than 1 must be an improper fraction. But if it is lesser than 1 would be a proper fraction.

For example: 0.25 = 0 + 0.25 = ${0+\dfrac{1}{4}}$= ${\dfrac{1}{4}}$ , it is proper fraction. So we can’t convert it to mixed number.

So, 3.25 = ${\dfrac{325}{100}}$, numerator > denominator, so it is an improper fraction. It can be changed to a mixed number.

${=3\cdot 25=3\dfrac{1}{4}}$

Solved Examples

Convert 5.86 to a mixed number.


5.86 = 5 + ${\dfrac{86}{100}}$
= ${5+\dfrac{43}{50}}$

Write 130.2 in mixed numbers.


5.86 = 130 + ${\dfrac{2}{10}}$
= ${130+\dfrac{1}{5}}$

Change 6.6 to mixed numbers.


6.6 = 6 + ${\dfrac{6}{10}}$
= ${6+\dfrac{3}{5}}$

Express 2.78 in mixed numbers


2.78 = 2 + ${\dfrac{78}{100}}$
= ${2+\dfrac{78}{100}}$
= ${2+\dfrac{39}{50}}$

Last modified on August 3rd, 2023

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