Mixed Fraction to Decimal

In order to convert a mixed fraction to decimal, we first change the mixed fraction to an improper fraction and then convert it to a decimal number. Let us learn more about converting a mixed fraction to decimal in this article.

Mixed Fraction to Decimal

Converting mixed fraction to decimal involves two simple methods. Before moving on to the conversion, let us recollect the definition of a mixed fraction and a decimal number. A mixed fraction, which is also known as a mixed number, is a fraction that has a whole number and a proper fraction. For example, \(2 \dfrac\) is a mixed fraction in which 2 is the whole number part and 1/4 is the proper fraction. A decimal is a number that has a whole number part and a fractional part that is separated by a dot called the decimal point. For example, 3.26 is a decimal number in which 3 is the whole number part and .26 is the fractional part.

How to Convert Mixed Fraction to Decimal?

There are two methods that can be used to convert mixed fractions to decimal numbers.

• Method 1: Convert the given mixed fraction to an improper fraction and then divide the numerator by the denominator to get the decimal form of the fraction.
• Method 2: Keep the whole number part the same, and convert the fractional part to a decimal by dividing the numerator by the denominator.

Example 1: (Using Method 1)

Convert the given mixed fraction to a decimal fraction: \(6 \dfrac\)

Solution:

• Step 1: First, we need to convert \(6 \dfrac\) to an improper fraction. For this, we will multiply the whole number (6) with the denominator (5). This gives 6 × 5 = 30.
• Step 2: The product (30) is added to the numerator (2) which gives 30 + 2 = 32.
• Step 3: This number (32) will be the new numerator and the denominator will remain the same. So, the improper fraction will be 32/5.
• Step 4: Now, this improper fraction can be converted to a decimal if we divide the numerator by the denominator. This will result in, 32 ÷ 5 = 6.4. Therefore, \(6 \dfrac\) is written as 6.4 in the decimal form.

Example 2: (Using Method 2)

Convert the given mixed fraction to a decimal fraction: \(7 \dfrac\)

Solution: In this method, we will keep the whole number part the same, and convert the fractional part to a decimal by dividing the numerator by the denominator.

• Step 1: We will keep the whole number part aside and convert 1/4 to a decimal number. For this, we will divide 1 by 4. This gives 1 ÷ 4 = 0.25
• Step 2: Now, we will add the whole number part to this decimal number. This means \(7 \dfrac\) = 7 + 1/4 = 7 + 0.25 = 7.25

How to Convert a Decimal to a Mixed Number?

In order to convert a decimal number into a mixed number, we first need to observe the number to the left of the decimal. If it is zero, the resultant fraction will be a proper fraction. This means that 0.75 will result into a proper fraction after conversion. In case, the number to the left of the decimal is non-zero, then the decimal will convert to a mixed fraction. This means that 6.25 will result into a mixed fraction.

Let us see the steps that are used to convert a decimal number to a mixed number. Let us convert 6.25 to a mixed fraction.

• Step 1: Since the given decimal has 6 as its whole number part, we will retain the whole number as it is. Then, we will identify the place value of the right-most digit after the decimal point and write the denominator accordingly.
• Step 2: In the given decimal, the right-most digit, 5, is in the hundredths place. This means that we will write 100 in the denominator.
• Step 3: Now, we will write the fraction in which the numerator will be 25 since it is given to the right of the decimal point and 100 will be the denominator.
• Step 4: Therefore, the resultant fraction will be, 25/100. This can be further reduced to 1/4. So, 6.25 as a mixed fraction can be written as \(6 \dfrac\)

Check out the following pages related to Mixed Fraction to Decimal:

• Decimals
• Mixed Fractions
• Improper Fractions
• Types of Fractions

Mixed Fraction to Decimal Examples

Example 1: Convert the given mixed fraction to decimal: \(8 \dfrac\) Solution: Let us convert the mixed fraction to decimal by first converting it into an improper fraction. \(8 \dfrac\) can written as 44/5 in the improper fraction form. Now, we will divide 44 by 5 which will give, 44 ÷ 5 = 8.8. Therefore, the given mixed fraction is converted to a decimal and is written as 8.8

Example 2: Convert the given mixed fraction to decimal: \(10 \dfrac\) Solution: Let us convert the mixed fraction to decimal by keeping the whole number aside. Now, we will convert 7/8 to its decimal form. So, 7 ÷ 8 = 0.875 After this step, we will add the whole number part (10) to this decimal number. This means \(10 \dfrac\) = 10 + 7/8 =10 + 0.875 = 10.875

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Practice Questions

FAQs on Mixed Fraction to Decimal

How to Convert Mixed Fraction to Decimal?

Mixed fractions can be converted to decimal numbers using two methods. In the first method, we convert the mixed fraction to an improper fraction and then divide the numerator by the denominator to get the decimal form of the fraction. For example, to convert \(3 \dfrac\) to a decimal fraction, we convert it into an improper fraction which is 23/7. Then, we divide 23 by 7 which gives 23 ÷ 7 = 3.28. In the second method, we keep the whole number as it is, and convert the fractional part to a decimal by dividing the numerator by the denominator. For example, to convert \(4 \dfrac\) to a decimal number, we will keep 4 aside and convert 2/5 to its decimal form. This will give 2 ÷ 5 = 0.4. Now, we will add the whole number 4 to this decimal. In other words, \(4 \dfrac\) = 4 + 2/5 = 4 + 0.4 = 4.4

How to Convert a Decimal Number into a Mixed Fraction?

In order to convert a decimal number into a mixed fraction, we use the following steps. Let us understand this by converting 7.356 to a mixed fraction.

• Step 1: Since the given decimal has 7 as its whole number part, we will keep the whole number as it is. Then, we will identify the place value of the right-most digit after the decimal point and write the denominator accordingly.
• Step 2: In the given decimal, the right-most digit, 6, is in the thousandths place. This means that we will write 1000 in the denominator.
• Step 3: Now, we will write the fraction in which the numerator will be 356 since it is given to the right of the decimal point and we already have 1000 as the denominator.
• Step 4: Therefore, the resultant fraction will be, 356/1000. This can be further reduced to 89/250. So, 7.356 as a mixed fraction can be written as \(7 \dfrac\)

How to Convert 1 3/8 Mixed Fraction to Decimal?

In order to convert \(1 \dfrac\) to a decimal number, we will first convert it into an improper fraction which will be 11/8. Now, we will divide 11 by 8 which will be, 11 ÷ 8 = 1.375.

How to Convert 9 7/8 Mixed Fraction to Decimal?

There are two methods that are used to convert a mixed fraction to a decimal. Let us use the method in which the whole number is retained. So, in this mixed fraction 9 7/8, the whole number 9 will be kept aside and 7/8 will be converted to a decimal. This results in, 7 ÷ 8 = 0.875. Now, we will add the whole number 9 to this decimal which means, \(9 \dfrac\) = 9 + 7/8 = 9 + 0.875 = 9.875

Write the Mixed Fraction 4 2/7 as a Decimal.

To convert \(4 \dfrac\) to a decimal, we will first convert it into an improper fraction. This will be 30/7. Now, we will divide 30 by 7 to change it to its decimal form. So, 30 ÷ 7 = 4.285.