How to Convert Fraction to Decimal (Includes Quiz and Video)

Earlier we talked about how you can convert Decimal to Fraction, now we will learn how to convert any decimal to fraction. We will divide this into 2 parts. The first part will discuss only Base-10 Fraction Types, and then we will move to all other fraction types.

Optional Video: Watch it if you are still confused about Fractions and Decimals

How to Convert Any Base-10 Fractions to Decimal?

Note: Base-10 here means any number that can be divided by 10, like 10, 100, 1000, 10000, or any of such numbers.

Example: Let’s take an example of fraction ¹/₁₀

Solution:
To convert this, you just have to make sure that you write 1 in the ten’s place and then put a decimal before 1 and 0 in the one’s place. So it will be 0.1 after converting ¹/₁₀ into decimal.

Another Example: Convert ²/₁₀₀ to decimal

Solution:
Just like we previously did, this time we are going to put 2 in the hundred’s place because we have 100 as the denominator. Since we don’t have any number before 2, we will fill ten’s place with 0 and then put decimal before 0. Finally, 0 will always be there in one’s place whenever we don’t have any number there. (We will show a couple of examples later when you don’t have to put 0 in one’s and ten’s place. So after conversion ²/₁₀₀ will be 0.02

Example (when 0 is not in one’s and ten’s place): Convert ²²³/₁₀₀ to decimal

Solution: ²²³/₁₀₀ will be 2.23 after conversion, but how? Read explanation below

Explanation (like a cheat code):

Always look at the denominator carefully. Count the zeroes it has. For example, if the denominator has 2 zeroes (means 100), the decimal must be placed after 2 digits (from the right). So the fraction ²²³/₁₀₀ has 100 (00 zeroes as the denominator), now place decimal after 2 digits from the right. It will be 2.23.

In case of ²³/₁₀ , it will be 2.3 because we only have 1 zero in denominator, so we will place decimal after first digit from the right.

if we want to convert ⁴⁹⁶/₁₀₀₀₀ to decimal, we need to place decimal after 4 digits from the right. Since we have only 3 digits, we have to use 1 zero. So it will be 0.0496

Important Note: Writing 0 in one’s place right before decimal is not a mandatory thing to do, for example, 0.0496 can be written as .0496 and it will still be correct. However, putting 0 right before decimal is a proper way (rather standard way) to write it. So I would recommend that you stick to this version: 0.0496

A Video to explain even further (Base-10 Fractions to Decimal)

How to convert any Fraction to Decimal

The conversion of Fraction to Decimal is always achieved by division, even Base-10 Fractions that we talked about above. However, we didn’t even talk about division while converting Base-10 Fractions to decimals because we had the easiest way to achieve this.

Question: How would you convert ¹/₂ to decimal?

Answer: since 1 cannot be divided by 2, we have to put 0 right after one (at ten’s place). However, where did the 0 come from? We will have to use a decimal right before the divisor since we put a zero right after 1.

So, ¹/₂ will become .5 or 0.5

Tip: Whenever the numerator is less than the denominator, we use decimal before divisor and then assume that the numerator has a zero at ten’s place. Decimal can be used just once, but if one zero is not enough and the numerator is still lower than the denominator, we then use a zero after numerator, Let’s see an example below.

Question: Convert ³/₁₀₀ to decimal.

Answer: So if we use decimal before divisor, this 3 will only be 30 that is still lower than the denominator (100). So we will have to use a 0 also before the divisor since 2 decimals cannot be used. So, before we start dividing we already have decimal and zero (.0) before the divisor that now made the numerator 300. Now ³⁰⁰/₁₀₀ = 3. We also had to put .0 before divisor, so it will be .03 or 0.03

What about those numerators that cannot be divided completely even after putting decimals?

Yes, there are many fractions that you cannot divide completely or it goes really a long way if you want to do that. In such cases, we usually stop trying to divide 3 digits after the decimal. For example, if we already have 0.346 and the numerator isn’t completely divided, we will stop right there. It’s the standard way to do things, if you want to keep trying even after that, that’s okay, and you can even do till 4, 5, or 6 digits, no one usually goes beyond that unless doing some kind of complex calculations.

Sorting Decimals with more than 2 digits after decimal

Whenever a decimal has more than 2 digits after decimal it is sorted to keep just 2 digits after decimal, but sorting isn’t done just by removing last digits.

If the third digit after the decimal is 5 or more than 5, the second digit will be increased by +1.
If the third digits after decimal is 4 or less than 4, we will simply remove 3rd digit.

For example:
0.346 will be sorted as 0.35
0.564 will be sorted as 0.56
0.459 will be sorted as 0.50 or 0.5
0.349 will be sorted as 0.35
0.67348 can be sorted as 0.6735 or 0.67 (it depends on how many digits you want to use after decimal – Minimum 2, but the maximum can be anything).

Question: Convert ³/₁₁ to decimal.

Answer:

• Since 3 is smaller than 11, we have to use decimal before divisor, and now we have 30. (Divisor so far: . )
• So 30 can now be divided by 11 (not completely, though). 11×2 = 22, so we will have 8 left. (Divisor so far: .2 )
• We can assume another zero after 8 that will not require putting 1 more decimal. This can keep going this way. So now we have 80. 11×7 = 77, so we have 3 left. (Divisor so far: .27 )
• We can now assume another zero after 3 that makes it 30. 11×2 = 22, we will now have 8 left. (Divisor so far: .272 )
• Since we have already reached 3 digits after the decimal, we are going to stop it here.
• After sorting .272, it will be .27 or 0.27 (hope you have already read about sorting that we explained above).
• So our answer is 0.27.

You can also try this Fraction to Decimal Converter tool to make sure you have got the correct answer. So solve problems and check answers.

Watch this Video to Learn More

Fraction to Decimal Quiz

Now you have learned the way to convert Fraction to Decimal, let’s try this quiz and test your skill. You have to click on the correct answer to score.