# Convert fractions to decimals - tasks & online exercises

## Convert fractions to decimals - introduction and repetition

Convert fractions to decimal numbers

Convert decimal numbers to fractions

**How do you calculate with decimal numbers or decimal fractions? **

In this section we learn how to convert decimal fractions into fractions and how to calculate with these decimal fractions. When calculating with quantities, we have already encountered many terms.

**1 decimetre = 1 tenth of a metre = \( \frac {1}{10} m \)****1 centimetre = 1 hundredth of a metre = \( \frac {1}{100} m \)****1 millimetre = 1 thousandth of a metre = \( \frac {1}{1000} m \)**

**Exercise 1 to start: Fractions and comma notation**

**Drag the correct solution to the spaces provided!**

**a) Fractions of sizes**Drag the fractions to the right place!

**b) Fractions in comma notation with decimal numbers**

Drag the decimal numbers to the right place!

## Decimal fractions Exercises 1 - Convert lengths

**c) Write the decimetres, centimetres, millimetres as metres!**First as a fraction, then with decimal numbers (in comma notation)

**Worksheets Decimal Fractions**

These tasks as a PDF for printing:

Select the language in the TOP menu to get the correct language on the worksheet!

## We convert fractions into decimal numbers

#### How to convert fractions into decimal numbers

**All fractions with a power of ten in the denominator can be written as a decimal fraction or decimal number!**

**Examples:**

**If there is no number of tens (power of ten) in the denominator, the following rule applies:**If you can reduce or expand the denominator of a fraction to a power of ten (tens 10, 100, 1000, ...), then the fraction can also be written as a decimal fraction.

**some examples:**

**Important denominators that can be well reduced to a power of ten:**

## Convert decimal numbers back to fractions

**The digits after the comma have a meaning!**

**See in the example: The number 0.375**

0.3 = 3 tenths

0.07 = 7 hundredths

0.005 = 5 thousandths

**0.375 = 3 tenths + 7 hundredths + 5 thousandths**

or:

\(\frac{3}{10} \overset{ \cdot \text{10}}{=}\frac{30}{100} \overset{ \cdot \text{10}}{=}\frac{300}{1000} \)

\(\frac{7}{100} \overset{ \cdot \text{10}}{=}\frac{70}{1000}\)

0.375 = \( \frac{300}{1000} + \frac{70}{1000} + \frac{5}{1000} = \frac{375}{1000}\)

**This is how you convert a decimal number into a fraction:**

Determine how many digits are behind the decimal point.

These digits tell you which number belongs in the** denominator**:

- with only 1 digit: 10 (tenths)
- with 2 digits: 100 (hundredths)
- with 3 digits: 1 000 (thousandth)
- with 4 digits: 10 000 (ten thousandths)
- keep it up!

All numbers before and after the decimal point are then placed on the fraction line, i.e. in the numerator of the fraction.

**Examples:**

(1) 2,705 => 3 Stellen hinter dem Komma = Tausendstel! alle Ziffern in den Zähler, 1000 in den Nenner: \( 2,705 = \frac{2705}{1000}\)

(2) 0,0074 => 4 Stellen hinter dem Komma = Zehntausendstel! Alle Ziffern in den Zähler, 10 000 in den Nenner: \( 0,0074 = \frac{74}{10000}\)

All right?

Then we can start with more exercises.

## Tasks - print online or as PDF

**Decimal fractions exercises (1)**

- Write as a decimal fraction!

**Convert fractions to decimal numbers (2) **

- Write as a decimal fraction!

**Decimal fractions exercises (3) **

- Convert the decimal fractions into fractions and shorten the result as much as possible!

**4 worksheets decimal fractions**

The tasks from these 4 exercises as a PDF to print out:

Select the language in the TOP menu to get the correct language on the worksheet!

**Decimal fractions tasks online (4) **

- Convert the fractions into decimal numbers. To do this, you have to shorten or expand the fraction first.

## Find the pairs - fractions and decimal fractions with the same value

## The book with many tasks for fractions: "Maths lesson 5 - Simple fractions".

The exercise book for getting started with fractions, with many decimal fractions tasks in one booklet!

**Maths lesson 5 - Simple fractions**

Exercise book for 5th grade / 6th grade

**Length:**60 pages, DIN A 4, stitched, b/w**Published:**2015**ISBN:**978-394186817-5**Price: 5,95 €**- Available everywhere in every bookshop (orderable) or in
*online shops*.