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Fractions and decimal fractions

You already know that there are numbers that lie on the number line between the whole numbers (e.g. between 0 and 1).

For prices you use decimal fractions (1.99 €), for quantities you use fractions ($$ 1/2 $$ kg strawberries). Mathematically, it doesn't matter whether you enter a value as a fraction or as a decimal fraction.


But how are the spellings related? How can you transform them into each other? Here we go:

Decimal fractions are also called decimal numbers. You can also say point numbers, but that's colloquial.

A quick reminder

This is what a break looks like

In the fraction $$ 4/5 $$ (read: four fifths) is that and that of. In between stands the Fraction line.

This indicates how many parts the whole has been divided into, or how big the parts are; so he named the parts.

This indicates how many of these parts are used; he used the parts.

So in the example above the whole thing has been broken up into parts, and parts of them have been used.

This is what a decimal fraction looks like

The best way to imagine a decimal fraction, such as $$ 36.45 $$, is in the place value table:
(z stands for tenths, h for hundredths)

Z E. z H number
$$3$$ $$6$$ $$4$$ $$5$$ $$36,45$$

The number $$ 36.45 $$ consists of $$ 3 $$ tens, $$ 6 $$ ones, $$ 4 $$ tenths and $$ 5 $$ hundredths.

Tenth? Hundredths? Sounds like breaks? Yes!

Z E. z H number
10 1 $$1/10$$ $$1/100$$
$$3$$ $$6$$ $$4$$ $$5$$ $$36,45$$

You can also simply say $$ 45 $$ hundredths for the digits after the decimal point.

How do you write a fraction as a decimal fraction?

Now the conversion: Expand or shorten the fraction until you have a Power of ten receive. Then you can write the fraction as a decimal fraction.

Example 1: Convert $$ 3/5 $$ to a decimal fraction.

The best way to expand $$ 3/5 $$ is to add $$ 2 $$.

$$ 3/5 stackrel (2) = (3 * 2) / (5 * 2) = 6/10 = 0.6 $$

$$ 6/10 $$ you say "six tenths". That makes a 6 in the tenth place of the decimal fraction.


Example 2: Convert $$ 1/25 $$ to a decimal fraction.

$$ 1/25 stackrel (4) = (1 * 4) / (25 * 4) = 4/100 = 0.04 $$


Example 3: Convert $$ 27/60 $$ to a decimal fraction.

Can't find a reduction or expansion number that leads to 10, 100, or 1000?

Sometimes it takes several steps to come up with a suitable denominator. Trick: First shorten with $$ 3 $$ and then expand with $$ 5 $$.



$$ 9/20 stackrel (5) = (9 * 5) / (20 * 5) = 45/100 = 0.45 $$

This is how you walk one Fraction into a decimal fraction around:
Expand or shorten until you have a power of ten in the denominator. The decimal fraction has as many decimal places as the denominator has zeros.

Powers of ten are the numbers $$ 10 $$, $$ 100 $$, $$ 1000 $$, $$ 10000 $$ etc.

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How do you write a decimal fraction as a fraction?

This transformation is even easier than the other direction. Everything you need can be read directly from the decimal fraction.

Example 1: Convert $$ 0.17 $$ to a fraction.

The decimal fraction $$ 0.17 $$ has 2 places after the decimal point.
You know that the second digit after the decimal point in the place value table is “hundredths”. 0.17 is the same as 17 hundredths.
As a fraction: $$ 17/100 $$


Further examples:

$$0,3 = 3/10$$

$$0,861= 861/1000$$

$$0,09=9/100$$


Examples with abbreviations:

If you can truncate fractions, always do that before moving on. Then you don't need to “juggle” large numbers.

$$0,250 = 250/1000 = 25/100 = 1/4$$

$$0,055=55/1000=11/200$$

When you convert a decimal fraction to a fraction, you see how many digits after the decimal point the decimal fraction has. That's the number of zeros in your power of ten fraction. As soon as possible.