Decimal numbers

Educational goal

In this course you are going to learn how to calculate with decimal numbers.

Prerequisites

• Fractions

• Written methods for multiplication and division

You've probably seen numbers like these in real life:

• A pair of socks costs $3.98$ euros

• Tom is $1.52\text{m}$ tall

• An apple crate weights $1.125\text{kg}$

Numbers like $3.98$, $1.52$ and $1.125$ are called decimal numbers.

You have probably dealt with place value chart before. If you want to set up a place value table for decimal numbers, you can simply extend it by decimal places. Example: $1589.736$ . The place value table can then be set up:

There is a problem: You could divide again and again without reaching a final result, the division remainder will always be 1. Therefore, your decimals will be 3.

Recurring decimal numbers

Decimal numbers like $0.3333333\dots$ are called recurring decimal numbers, because the same numbers keep recurring infinitely often. There is another way of notating $0.3333333\dots$ You can just write $0.\overline{3}$. Another recurring decimal number is $1.\overline{12}=1.121212\dots$ In this case, two numbers keep recurring.

The following sum occurs: $1+0.1+0.01+0.001+\dots$

Think about: $0.\overline{2}=\frac{2}{9},0.\overline{3}=\frac{3}{9}=\frac{1}{3},0.\overline{7}=\frac{7}{9},\text{and so on}$

1. Write the three successors of the summand 0.001. Describe how the sum is built up.

2. Calculate the value of the above sum.

3. Calculate: $3-0.2-0.02-0.002-...$

It is essential…..

Exercises

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Conversion …

exercise