# 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 simplyin the text
- Convert finite decimals to fractionsin the text
- Convert periodic decimal numbers to fractionsin the text
- Convert mixed periodic decimal numbers to fractionsin the text
- Important decimals as fractionsin 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:

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:

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 ...

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!

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