What you need to know

Things to remember:

  • Knowing basic fraction and decimal equivalents will make this easier.

What is 3\dfrac{3}{8} as a decimal?

To start, it is important to remember that 3\dfrac{3}{8}=3+\dfrac{3}{8}, i.e. a whole number and a fraction added together.

Hint: If we can learn some basic fraction equivalencies, we can use them to help us convert mixed numbers into decimals.

 

\frac{3}{4}=0.75

\frac{1}{2}=0.5

\frac{1}{4}=0.25

\frac{1}{5}=0.2

\frac{1}{8}=0.125

\frac{1}{10}=0.1

\frac{1}{20}=0.05

\frac{1}{50}=0.02

\frac{1}{100}=0.01

Now that we have these we can try and convert our mixed number into a decimal. We will do this in three steps.

Step 1: Choose the relevant fraction and decimal equivalent

Our mixed number is using eighths, so we want to use the equivalent decimal.

\frac{1}{8}=0.125

Step 2: Using the equivalent decimal in Step 1, convert your fraction into a decimal.

3\times\frac{1}{8}=3\times0.125

{3}{8}=0.375

Step 3: Add the decimal found in Step 2 to the whole number part of the mixed number.

3+0.375=3.375

3\frac{3}{8}=3.375

Converting decimals into mixed numbers is a little trickier, but we can follow similar steps as to what we did previously.

What is 5.3 as a mixed number?

Step 1: Split up your number into the whole number part and a decimal.

5.3=5+0.3

Step 2: Choose the relevant fraction and decimal equivalent.

Hint: This will get easier with practice and knowing multiples of the decimals and fractions.

 

0.3=3\times0.1

But we know that 0.1=\dfrac{1}{10}, so…

0.3=3\times0.1=3\times\frac{1}{10}=\frac{3}{10}

Step 3: Put the whole number part and fraction found in Step 2 together.

5.3 =5\frac{3}{10}

Example Questions

Question 1: What is 7\dfrac{2}{5} as a decimal?

Answer

Step 1: Choose the relevant fraction and decimal equivalent

 

Our mixed number is using fifths, so we want to use the equivalent decimal.

 

\frac{1}{5}=0.2

 

Step 2: Using the equivalent decimal in Step 1, convert your fraction into a decimal.

 

2\times\frac{1}{5}=2\times0.2

 

{2}{5}=0.4

 

Step 3: Add the decimal found in Step 2 to the whole number part of the mixed number.

 

7+0.4=7.4

 

7\frac{2}{5}=7.4

Question 2: What is 9.75 as a mixed number?

Answer

Step 1: Split up your number into the whole number part and a decimal.

 

9.75=9+0.75

 

Step 2: Choose the relevant fraction and decimal equivalent.

 

Hint: This will get easier with practice and knowing multiples of the decimals and fractions.

 

 

0.75=\frac{3}{4}

 

Step 3: Put the whole number part and fraction found in Step 2 together.

 

9.75 =9\frac{3}{4}