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# 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 sizesDrag 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

Decimal fractions tasks - conversion from fraction to decimal numberc) 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:
(1)   $$\frac{43}{100} = 0,43$$
43 hundredths = 0.43
(2)   $$\frac{124}{1000} =0,124$$
124 thousandths = 0.124
(3) $$\frac{2507}{1000} =2,507$$
2507 thousandths = 2.507
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:
(1)   $$\frac{3}{5} \overset{ \cdot \text{2}}{=} \frac{6}{10} =0,6$$(2)   $$\frac{9}{4} \overset{ \cdot \text{25}}{=} \frac{225}{100} =2,25$$(3)   $$\frac{8}{25} \overset{ \cdot \text{4}}{=} \frac{32}{100} =0,32$$
Important denominators that can be well reduced to a power of ten:
(1)   $$\frac{1}{2} = \frac{5}{10}$$
can be extended to tenths.
(2)   $$\frac{3}{4}, \frac{7}{20}, \frac{2}{25}$$
can be extended to hundredths
(3)   $$\frac{1}{16}$$
can be extended to ten thousandths with 625, because
$$16 \cdot 625 = 10000$$ .

## 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:

Decimal fractions tasks online (4)

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

## 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.