What is 1 2 as a fraction

Convert decimal number to fraction

You can learn here how to convert a decimal number (point number) into a fraction. Let's look at this:

  • A Explanationhow to convert decimal numbers to fractions.
  • Lots Examples to the various cases of conversion.
  • Tasks / exercises so that you learn to convert decimal numbers to fractions and vice versa.
  • A Video to decimals.
  • A Question and answer area to this area.

Note: Anyone interested in converting decimal numbers to fractions will usually already know what a fraction is and what a decimal number is. If not, please first look at the definition and fractions in decimal numbers (point numbers).

Explanation of the decimal number in fractions

How to convert a number (decimal) to a fraction? Unfortunately, we have to distinguish between three cases:

  1. Finite decimal number
  2. Purely periodic decimal number
  3. Mixed periodic decimal number

Let's start with the simplest case: The finite decimal number, i.e. the finite point number.

Convert a finite decimal number (point number) to a fraction:

In most cases you have a finite decimal number to convert. Examples of finite decimal numbers would be:


The conversion is very simple here:

  • The numerator contains the decimal number without a comma.
  • Write a 1 in the denominator.
  • After the 1 in the denominator, as many zeros as there are places behind the decimal point.

Let's just do this for these four numbers.

example 1:

Note: In some cases, fractions can still be shortened. You will learn how to do this by shortening fractions.


Examples of periodic decimal numbers

In this section we look at the procedures for pure-period decimal numbers and mixed-period decimal numbers. With periodic numbers, one or more numbers repeats over and over again.

Purely periodic decimal numbers:

What are periodic decimal numbers? Well, a purely periodic decimal number is a decimal number where the period starts right after the decimal point. These three decimal numbers would be purely periodic:


Procedure Convert periodic decimal numbers into fractions:

  • Write the whole number before the comma
  • Write plus sign
  • Adopt period information in counter
  • As many 9's in the denominator as there are digits in the period.
  • Turn everything into a fraction.

Example 2a:

First, 0.333 ... is to be converted into a fraction. We have a zero in front of the decimal point, we take it over. Then we have a period with 333, which we take over into the counter. These are also 3 digits, so we write 9 in the denominator three times.

We can also omit the 0 in front. There remains 333: 999. We have thus completely converted into a fraction. If you like, you can shorten this fraction.

Example 2b:

Now 2.424242 ... is to be converted. We write the 2 down and a plus sign. The period consists of 42, which we write in the counter. These are also 2 digits, so we write the 9 twice in the denominator.

We can make a total break out of it. To do this, we multiply the 2 by 99 and divide by 99. This enables us to calculate the counters.

Example 2c:

Another example with 8.9417 ... We first split off the 8. We write the four digits after the decimal point (period) into the numerator. Because of 4 digits in the numerator, we write four 9's in the denominator. Then we summarize by calculating the 8 in front with 9999: 9999. This allows us to calculate in the numerator 8 9999 + 9417 = 89409, the 9999 remains in the denominator.

Convert mixed periodic decimal numbers to fractions:

We still lack the mixed-period numbers, which are to be converted into a fraction. These are decimal numbers with one or more numbers after the decimal point and only then does the period start. These would be mixed period decimal numbers:


Procedure for mixed-period decimal numbers in fractions:

  • Multiply the decimal number by 10 until there is only the periodic part after the decimal point.
  • Convert like a whole period number.
  • Undo the first step.

Example 3:

It is supposed to be converted into a fraction 2.1343434 ... We have a place after the decimal point that does not belong to the period. Since it's only one digit, we multiply by 10.

We separate everything before the comma. Then a plus sign. Write on the fraction after it as in the numerator 34. The 34 has two digits, hence the 9 twice in the denominator.

We summarize this: To do this, we multiply 21 by 99 and divide by 99 again. What is this about? So we can easily summarize in the numerator: 21 · 99 + 34 = 2113 while the 99 remain in the denominator.

We multiplied by 10 at the beginning. So now we have to divide by 10. We do this by adding a 0 in the denominator. We obtain:

Example 4:

Here is the quick calculation for 0.478181 ... We have two places behind the decimal point that do not belong to the period. Therefore, we first multiply by 100 and then divide by 100 again at the very end.

Tasks / exercises Convert decimal numbers


Videos decimals

Calculating with decimal numbers

We don't have a direct video on how to convert decimals to fractions yet. However, you should still be able to calculate with decimal numbers. So we see this in the video:

  1. Definition of decimal numbers
  2. Addition of decimal numbers
  3. Subtraction of the decimal point
  4. Multiplication of decimal numbers
  5. Division of decimal numbers

Next video »

Questions with answers number in fraction

In this section, we'll look at typical questions with answers about decimals and fractions.

Q: How does the reverse case work: converting a fraction into a decimal number?

A: A fraction is just like dividing numbers. Therefore, you can also go the other way around and convert a fraction into a decimal number. You can learn how to do this under Fractional Numbers.

Q: How does calculating with decimal numbers work?

A: You should learn to calculate with decimal numbers (point numbers). These are the basic arithmetic operations of addition, subtraction, multiplication and division. You should also master a mixture of these basic arithmetic operations. You can find many explanations and examples under Calculating decimal numbers (point numbers).