Mixed Number to Decimal

Conversion of a mixed number to decimal is important to learn to find the precise values of mixed numbers. Mixed number to decimal conversion is done by converting the mixed fraction to an improper fraction first and then dividing the numerator by the denominator. This is just one way to do the conversion. Let us learn all the methods of conversion of a mixed number to decimal in this article.

There are two methods to convert a mixed number to decimal form:

• By converting the mixed number to an improper fraction.
• By converting only the fractional part of the given mixed number to decimal and then adding the whole number part to it.

Method 1: In this method, we first find the improper fraction of the given mixed number. Then we divide the numerator by the denominator to find its decimal equivalent. For example, \(2\dfrac{2}{3}\) can be converted to an improper fraction as,

\(2\dfrac{2}{3}\) = [(3 × 2) + 2]/3 = 8/3

Now, if we divide 8 by 3, we will get 2.67 approximately. Therefore, the decimal equivalent to the mixed number \(2\dfrac{2}{3}\) is 2.67. Let us use the same example to understand the second method.

Method 2: In this method, we will keep the whole number part aside and convert only the fractional part of the mixed number to decimals. So, in the given number \(2\dfrac{2}{3}\), the fractional part is 2/3, which can be converted to decimal as 2 ÷ 3 = 0.67 (approximately). Now, let us add the whole number part to it. So, we will get 2 + 0.67 = 2.67. Therefore, \(2\dfrac{2}{3}\) = 2.67. Irrespective of the method used, the answer of a mixed number to the decimal conversion will always be the same.

Observe the figure given below which shows the mixed number to decimal conversion of \(5\dfrac{6}{7}\).

You can also use Cuemath's free online mixed number to decimal calculator to verify your answers.

We can convert a decimal to a mixed number using the same concept that is used to convert a mixed number to decimal form. To convert a decimal to a mixed number, we follow the steps given below:

• Step 1: Count the number of decimal places in the given number.
• Step 2: Remove the decimal point and divide the number by a power of 10 equal to the number of decimal places. So, if there are 2 decimal places, it means we have to divide the number by 10² which is 100. In other words, the number of zeros should be equal to the number of decimal places.
• Step 3: Simplify the fraction and if it is an improper fraction, convert it into a mixed number.

For example, let us convert a decimal number 2.5 to a mixed fraction.

☛ Related Articles

Check these interesting articles related to the concept of mixed number to decimal conversion in math.

• Improper Fraction to Mixed Number
• Mixed Number to Improper Fraction
• Convert Decimal to Fraction
• Fraction to Decimal

What is Mixed Number to Decimal Conversion?

Mixed number to decimal conversion in math is useful to find the decimal equivalents of mixed fractions. This is done by converting the mixed number to an improper fraction and then dividing the numerator by the denominator.

How to Change a Mixed Number to Decimal?

To change a mixed number to decimal form, we find the decimal value of the fractional part of the number and then add it to the whole number part. For example, \(1\dfrac{4}{5}\) can be converted to decimal in the following way. This means, 1 + 4/5 = 1 + 0.8 = 1.8

How to Write a Decimal into a Mixed Number?

To convert a decimal to a mixed number, we divide the decimal number by a power of 10 equal to the number of decimal places in the given number.

For example, let us convert 1.25 to a mixed number using the following steps:

• Step 1: First we need to count the number of decimal places in the given number. Here, there are 2 decimal places in 1.25
• Step 2: Then we remove the decimal point and divide the number by a power of 10 which is equal to the number of decimal places. Since there are 2 decimal places, it means we need to divide the number by 100. Here, after removing the decimal, we get, 125/100
• Step 3: After this step, the fraction can be simplified and if it is an improper fraction, it can be converted to a mixed fraction. Here, after simplifying 125/100 we get 5/4 and then 5/4 = \(1\dfrac{1}{4}\)

What is 6 1/4 Mixed Number to Decimal?

Let us convert \(6\dfrac{1}{4}\) to a decimal. This can be written as 6 + 1/4. The decimal value of 1/4 is 0.25. So, we have 6 + 0.25, which is equal to 6.25. Therefore, \(6\dfrac{1}{4}\) is equal to 6.25.

What are the Steps to Convert Mixed Number to Decimal?

The steps of conversion of mixed number to decimal are written below:

1. Convert the mixed number to an improper fraction.
2. Divide the numerator by the denominator to get the value in decimals.