What is 9 in decimal places

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 speaking, 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.

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 conversion 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 places after the decimal point the decimal fraction has. That's the number of zeros in your power of ten fraction. As soon as possible.