How to Convert Fractions to Decimals (& Vice Versa)

Nov 8, 2024 | La Costa
Mathnasium tutor helping a student.

Decimals and fractions are two different ways, or formats, to express quantities. You can think of them as two sides of the same coin!  

Whether you’re following a recipe that calls for \( \Large \frac{1}{2}\) liter of milk or 0.75 cup of sugar, or you are measuring lengths such as 1.5 meters or 1\( \Large \frac{2}{3}\) yards, you will see these formats used almost interchangeably. 

But, how do you keep track of fractions and decimals when they appear in the same recipe, for example?  

It’s simple! We convert all values into the same format. 

In this guide, you’ll find easy-to-follow steps to converting fractions to decimals (and vice versa) with simple definitions, solved examples, and a practice test. 

Enjoy! 

Meet the Top-Rated Math Tutors in La Costa, Carlsbad

First, A Quick Recap: What Are Fractions & Decimals? 

Fractions and decimals are ways to represent parts of a whole or parts of whole numbers. 

A fraction is a way to show a part of something by dividing it into equal pieces. It has two parts: 

  1. Numerator: The top number, which tells you how many parts you have. 
  2. Denominator: The bottom number, which tells you how many equal parts the whole is divided into. 

For example, in the fraction \( \Large \frac{3}{4}\), the numerator is 3 indicates that we have 3 parts of a whole which consists of 4 parts, as indicated by denominator. 

A decimal is another way to represent fractions but based on powers of 10. Decimals use a decimal point to separate the whole number from the fractional part. 

For example, the fraction \( \Large \frac{1}{2}\) can also be written as the decimal 0.5.  

Here: 0 is the whole number part, while .5 is the decimal part. 

Decimals are especially useful in calculations and measurements as they are often easier to add, subtract, multiply, and divide than fractions.  

Both fractions and decimals give us a flexible way to work with numbers that aren't whole. 

Graphic demonstrating a fraction vs a decimal


How to Convert Fractions to Decimals? 

There are two main methods you can use to convert fractions to decimals: 

  1. Long Division Method: Divide the numerator by the denominator using long division. 
  2. Denominator Conversion Method: Convert the denominator to a power of 10 (like 10, 100, or 1,000) and adjust the fraction accordingly. 

The Long Division Method  

The most commonly used method to convert a fraction to decimal without a calculator is long division.  

To do this, remember the steps you learned from long division: 

  1. Divide: Find out how many times the divisor fits into the dividend. 
  2. Multiply: Multiply the divisor by that number. 
  3. Subtract: Subtract the result from the dividend. 
  4. Bring Down: Bring down the next digit from the dividend. 
  5. Repeat: Continue the steps until there are no more digits to bring down.

Let’s follow these steps to convert \( \Large \frac{3}{4}\) to a decimal.  

Step 1: Set Up the Division Task  

Set up the fraction as a division problem, with 3 (numerator) as the dividend and 4 (denominator) as the divisor. 

Step 2: Add a Decimal Point 

Our divisor 4 is smaller than the dividend 3 which means that the number of times it goes into it is 0.  

Add 0. to your quotient. 

Then, add a .0 after the dividend: 3.0.  

To make the next step easier, we will represent the dividend 3.0 as 30. 

Step 3: Divide 

Check how many times 4 goes into 30.  

Since 30 isn’t divisible by 4, we can find the number closest to 30 that’s divisible by 4 which is 28. 

28÷4=7 

We see that 4 goes into 30 a total of 7 times.  

Write 7 after the decimal above the division bar. 

Step 4: Multiply 

Now multiply 7 by the divisor (4). 

7×4=28 

Write 28 below the dividend. 

Step 5: Subtract 

Subtract 28 from 30 and write the result below. 

30−28=2 

 Step 6: Bring Down 

Since 4 (the divisor) can’t fit into 2, we add another zero to the dividend to make it 3.00.  

Then we bring the zero down, next to 2 and make it 20. 

Step 7: Divide Again 

Check how many times 4 goes into 20.  

20÷4=5 

This shows us that 4 fits into 20 a total of 5 times.  

Write 5 next to 7 in the quotient above the division bar. 

Step 8: Multiply Again 

Multiply 5 by 4 and write the result below. 

5×4=20  

Step 9: Final Subtraction 

Subtract 20 from 20. 

20−20=0  

 

Since there is no remainder, we will stop here.  

The final answer is: \( \Large \frac{3}{4}\) = 0.75

Denominator Conversion Method

Another method to convert fractions to decimals is to change the denominator to a power of 10, such as 10, 100, or 1,000. 

Note that this method only works for fractions where the denominator can be adjusted to reach a power of 10. 

Let's use this method to convert \( \Large \frac{3}{5}\) to a decimal: 

Step 1: Find the Multiplier  

Find what number to multiply the denominator 5 by to reach the closest power of 10.  

This would be:  

5×2=10 

So, our multiplier is 2. 

Step 2: Multiply the Fraction 

Now, multiply the denominator and the numerator by this number (2). 

\( \Large \frac{3x2}{5x2}\)=\( \Large \frac{6}{4}\)

Step 3: Convert the New Fraction to a Decimal 

Now, we have a new fraction, \( \Large \frac{6}{10}\), we can convert it to a decimal. 

We check how many zeroes the denominator has. Since 10 has one zero, we place the decimal one place to the left.  

So, \( \Large \frac{6}{10}\) becomes 0.6. 

Similarly, if the denominator had two zeros, we would get 0.06. If it had four zeros, we would get 0.0006 and so on.  

Could we apply this method to a fraction like \( \Large \frac{2}{3}\)

No, because the denominator 3 cannot be adjusted to reach a power of 10. 

How to Convert Decimals to Fractions? 

Converting decimals into fractions is usually simpler than the other way around. The logic is simple: 

  • Digital before the decimal point are whole numbers. 
  • Digits behind the decimal point and zeros (if any) are numerators. 
  • The powers of 10 are your denominators and we determine them based on the number of zeros we see after the decimal point. 

Let’s convert 0.7 into a fraction. 

Step 1: Find Where the Decimal Ends 

First, look at where the decimal ends. 

In our case, 0.7 ends in the tenths place. 

Step 2: Make the Fraction 

The place where the decimal ends becomes your denominator.  

Since our decimal ends in the tenths, our denominator will be 10.  

The digit behind the decimal point and zeros (if any) becomes your numerator.  

So, by converting 0.7 into a fraction, we get: \( \Large \frac{7}{10}\).

Step 3: Simplify if Necessary  

Finally, check if the fraction can be simplified.  

In this case, \( \Large \frac{7}{10}\) is already in its simplest form! 


Converting Decimals with Whole Numbers 

When a decimal has both a whole number and a fractional part (e.g. 1.25, 2.5, 3.2, and so on), the principle of conversion remains the same, with one additional step. 

Let’s try to convert 1.66 into a fraction. 

Step 1: Separate the Whole Number and Decimal 

For 1.66, the whole number is 1, and the decimal is 0.66. 

Step 2: Find Where the Decimal Ends 

Check where the decimal ends. 

In this case, 0.66 ends in the hundredths.  

Step 3: Make the Fraction  

The place where the decimal ends becomes your denominator. 

Since 0.66 ends in the hundredths, the denominator is 100. 

The digit behind the decimal becomes the numerator. In this case, it’s 66. 

So, we will have \( \Large \frac{66}{100}\).

Step 4: Simplify if Necessary   

Finally, check if the fraction can be simplified.  

In this case, both 66 and 100 are divisible by 2. 

\( \Large \frac{66÷2}{100÷2}\)=\( \Large \frac{33}{50}\)

Finally, the decimal 1.66 is equivalent to the mixed number 1 \( \Large \frac{33}{50}\)

Solved Examples for Decimal and Fraction Conversions 

Let’s see a few more examples that illustrate how converting decimals and fractions works. 

Example 1 

Let's convert \( \Large \frac{2}{3}\) using the long division method.  

Step 1: Set Up the Division Task 

Set up the fraction as a division problem, with 2 (numerator) as the dividend and 8 (denominator) as the divisor. 

Step 2: Add a Decimal Point 

Since 8 can’t go into 2, place a 0 and a decimal point in the quotient. 

Place a decimal point after 2 (the dividend) and add a zero to make it 2.0. We will now treat the dividend as 20 for easier calculations. 

 Step 3: Divide 

Check how many times 8 goes into 20.  

Since 20 isn't divisible by 8, let's find the number closest to 20 that is divisible by 8. That number is 16. 

16÷8=2 

So, 8 goes into 20 a total of 2 times. We place the 2 above the division bar in the quotient, right after the decimal point. 

Step 4: Multiply 

Now multiply 2 by the divisor (8). 

2×8=16 

Write 16 below the dividend. 

Step 5: Subtract 

Subtract 16 from 20. 

20−16=4 

Write the result below.  

Step 6: Bring Down 

Since 8 cannot go into 4, add another zero to the dividend (2.00) and bring it down next to 4. 

Step 7: Divide Again 

Check how many times 8 goes into 40. 

40÷8=5 

Write 5 next to 2 in the quotient. 

Step 8: Multiply Again 

Multiply 5 by 8 and write the result below. 

5×8=40 

Step 9: Final Subtraction 

Subtract 40 from 40. 

40−40=0  

Write the result below. 

Since there is no remainder, we will stop here. 

The final answer is: 

\( \Large \frac{2}{8}\)=0.25

Example 2 

Convert  to a decimal using the denominator conversion method. 

Step 1: Find the Multiplier 

Find what number to multiply the denominator (8) by to reach the closest power of 10. 

This would be: 

8×125=1000 

Step 2: Multiply the Fraction 

Now, multiply the denominator and the numerator by the same number (125). 

\( \Large \frac{5x125}{8x125}\)=\( \Large \frac{625}{1000}\)

Step 3: Convert the New Fraction to a Decimal 

Check how many zeroes the denominator has. Since 1,000 has three zeroes, we place the decimal three places to the left.   

\( \Large \frac{625}{1000}\)=0.625

So, \( \Large \frac{5}{8}\) converts to 0.625. 

Example 3 

Convert the decimal 0.025 to a fraction. 

Step 1: Find Where the Decimal Ends 

With three digits after the decimal point, 0.025 ends in the thousandths place. 

Step 2: Make the Fraction 

The place where the decimal ends becomes the denominator. 

Since 0.025 ends in the thousandths, the denominator will be 1,000. 

The digits behind the decimal become the numerator. In this case, it’s 25. 

Put the two together and our fraction is \( \Large \frac{25}{1000}\).

Step 3: Simplify Fraction 

Check if the fraction can be simplified. 

Both the numerator (25) and the denominator (1,000) are divisible by 25. 

\( \Large \frac{25÷25}{1000÷25}\) =\( \Large \frac{1}{4}\)

0.025=\( \Large \frac{1}{40}\)

 Example 4  

Let’s convert a decimal that consists of a whole number:  

4.85 

Step 1: Separate the Whole Number and the Decimal 

First, separate the whole number from the decimal.  

In this case, 4 is the whole number, and 0.85 is the decimal part. 

Step 2: Find Where the Decimal Ends 

The decimal 4.85 has two digits after the decimal point, so it ends in the hundredths place. 

Step 3: Make the Fraction 

The place where the decimal ends becomes the denominator. In this case it is 100.  

The digits behind the decimal become the numerator. In this case, it’s 85. 

So, the fraction will be \( \Large \frac{85}{100}\).

Step 4: Simplify If Necessary 

Next, simplify \( \Large \frac{85}{100}\). Both numbers are divisible by 5. 

\( \Large \frac{85÷5}{100÷5}\)=\( \Large \frac{17}{20}\)

We bring the whole number and the fraction together to form a mixed number: 4\( \Large \frac{17}{20}\).

Test Your Skills and Try Converting Yourself! 

It’s your turn!  

Try these practice examples on your own and scroll to the end of the guide to check your answers. 

Exercise 1 

Convert the fraction \( \Large \frac{4}{5}\) to a decimal using the long division method. 

Exercise 2 

Convert the fraction \( \Large \frac{1}{8}\) to a decimal using the denominator conversion method. 

Exercise 3  

Convert the decimal 0.035 to a fraction. 

Exercise 4  

Convert the decimal 7.45 to a fraction. 

Master Decimals and Fractions with Top-Rated Math Tutors in La Costa, Carlsbad 

Mathnasium of La Costa is a math-only learning center in Carlsbad, CA, for K-12 students of all skill levels, including elementary schoolers.  

Find us at 3451 Via Montebello, #190, Carlsbad, CA 92009. 

Discover our approach to elementary school tutoring:  

Whether your student is looking to catch up, keep up, or get ahead in their math class, find a Mathnasium Learning Center near you, schedule an assessment, and enroll today! 

Schedule a Free Assessment at Mathnasium of La Costa 

Psst! Check Your Answers 

If you have given our exercises a go, check your answers here: 

Exercise 1: 0.8 

Exercise 2: 0.125 

Exercise 3: \( \Large \frac{7}{200}\)

Exercise 4: 7\( \Large \frac{9}{20}\)