What is half of Frac 57 74

Decimal number in fractions

We'll show you how to convert a decimal number to a fraction.

  • Converting decimal numbers to fractions explained simply
    in the text
  • Convert finite decimals to fractions
    in the text
  • Convert periodic decimal numbers to fractions
    in the text
  • Convert mixed periodic decimal numbers to fractions
    in the text
  • Important decimals as fractions
    in the text
  • in the text

Converting decimal numbers to fractions explained simply

How you convert a decimal number to a fraction depends on what type of decimal number you have. You have to differentiate between the following types:

  • finite decimal numbers (e.g. )
  • periodic total numbers (e.g. )
  • mixed periodic decimal numbers (e.g. )

Now let's take a close look at how to do that!

Convert finite decimals to fractions

If you want to convert finite decimal numbers (e.g. 2.487 or 0.2) into fractions, you proceed as follows:

Finite decimal number in fractions

Step 1: Insert the number without a comma in the counter

Step 2: Write a one under the fraction line

3rd step: Add as many zeros to the denominator as there are decimal places

example 1

Imagine you want to convert decimals to fractions and you have the number 2,487.

1. Insert the number without a comma in the counter:

2. Write a one under the fraction line:

3. Add as many zeros to the denominator as there are decimal places:

So you can put the decimal number 2.487 in the fraction convert.

Example 2

You want to convert the number 0.6605 to a fraction.

1. Insert number without comma in the counter:

2. Write one under the fraction line:

3. Add as many zeros to the denominator as there are decimal places:

You have 0.6605 in the fraction transformed.

Further examples

Now you know how to convert finite point numbers into fractions! After you have converted a decimal number into a fraction, you can usually shorten it. For the sake of simplicity, we will omit these examples.

Convert periodic decimal numbers to fractions

In the case of periodic decimal numbers, the numbers after the decimal point are repeated infinitely often:

Periodic decimal number in fractions

1st step: Split off whole number

Step 2: insert the period in the counter

3rd step: In the denominator, add the 9 as often as there are places below the period line

4th step: Add up fraction and whole number

example 1

Take a look at an example of how this works: Imagine you want the decimal number convert to a fraction:

1. Split off whole number

2. Set period in counter:

3. In the denominator, add the 9 as often as there are places below the period line:

4. Add fraction and whole number together:

Example 2

You want the decimal convert to a fraction.

1. Split whole number:

There is no whole number in front of the comma. Therefore, you can go straight to the next step.

2. Insert period in numerator of fraction:

3. In the denominator, add the 9 as often as there are places below the period line:

4. Add fraction and whole number together:

In the first step, you did not separate a whole number that you could add up here. That's why you can skip the last step.

You have the number can convert into a fraction. It reads .

Great, now you can easily convert a periodic decimal number to a fraction!

Convert mixed periodic decimal numbers to fractions

In the case of mixed-period numbers, only the last part after the decimal point, which is below the period line, is repeated. The number can therefore be written as 3.3848484 ...

Mixed periodic number in fraction

Step 1: Multiply the number by 10 until only the periodic sequence of numbers is behind the decimal point

Step 2: split off period from number

Step 3: Convert both parts to fractions with the same denominator

4th step: add both fractions together

Step 5: Divide the total fraction by ten as often as you multiplied it at the beginning.

example 1

To better understand this process, take a look at the following example: You want the decimal number convert to a fraction.

1. Multiply the number by 10 until only the periodic sequence of numbers is behind the decimal point:

2. Split period from number:

3. Convert both parts to fractions with the same denominator:

4. Add up both fractions:

5. You multiplied the number by 10 twice at the beginning. So now you have to divide it twice by ten.

Done! You have the decimal in the break can convert.

Example 2

You want to convert to a fraction.

1. Multiply the number by 10 until only the periodic sequence of numbers is behind the decimal point:

2. Split period from number:

3. Convert both parts to fractions with the same denominator:

4. Add up both fractions:

Respect, you are now ready to convert decimal numbers into fractions!

Important decimals as fractions

There are some important decimal numbers whose fractions you need to know about. If you know them, you will be well prepared for your next tasks!

Finite decimal numbers:

Periodic decimal numbers:

Fraction in decimal number

In assignments, you will often need to convert fractions to decimal numbers. But how does it work? To find out, you have to watch our video!