What does zero mean?

Old acquaintances in a new light

Numbers with commas! You already know them from prices.

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In the advertisement, 1.5 kg of potatoes are said to cost 1.59 euros, which corresponds to a price of 1.06 euros per kg.

Here are more examples with decimal points:

  • You are maybe 1.48 m tall.
  • The sprinter Usain Bolt holds the world record in the 100 m sprint with 9.58 s.

Image: Picture-Alliance GmbH (landov)

Mathematicians would grumble about this notation "1 kg = 1.06". That = is wrong here.

For this there is the sign "corresponds":

1 kg € 1.06

Better to write the sign in math class. :)

Decimal fractions

Floating numbers are usually not natural numbers, but fractions. 1.5 is between 1 and 2. The whole is before the comma (1), the part of the whole after the comma (0.5).

The place value table

Our number system is the decimal system (also decimal system or decimal system).

That means: You can write down any number using the 10 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Fractional numbers too!

You expand the value board to the right.

example: 12,87

The comma is to the right of the units digit, the decimal point is followed by tenths, hundredths and thousandths.

Decimal fractions are also called decimal numbers. Point numbers are more colloquial.

decem (Latin) "ten"

Create a place value board

Always keep the place value table in mind when dealing with decimal fractions.
In this expanded place value table you can see the connection between the spelling and the fractions.

Example:200,05 , pronounced “two hundred point zero five”.

Spelling with fractions of ten

This is how you can "translate" decimal fractions:

$$ cdot $$ $$200,05 = 200 + 0/10+5/100$$

$$ cdot $$ $$1,596 = 1 + 5/10 + 9/100 + 6/1000$$

$$ cdot $$ $$0,102 = 0 + 1/10 + 0/100 + 2/1000$$

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Correct pronunciation

With point numbers, you read the digits to the right of the point from left to right, without the names of the place values.

numberThat's how you read it
0,63 Zero point six threeZero point sixty-three
127,03 One hundred twenty-seven point zero three One hundred and twenty-seven point three
200,30Two hundred point three zeroTwo hundred point thirty
0,00708Zero point zero zero seven zero eightZero point zero zero seven hundred eight

Zero equals nothing?

A place value system does not work without the number zero.

The zero in the place value system

In a place value system, zeros help indicate the place value of the remaining digits.

You already know this from natural numbers: With natural numbers, the last digit is always the ones digit. If the ones digit is zero, the number is divisible by 10.

5Z = 5Z 0E = 50

In the case of decimal numbers, the comma indicates the position of the units digit. The comma is always to the right of the units, before the tenths.

For example, if you have 1T (ausender) and 1 z (tenth), there are zeros in all places between these positions.

1T 1z = 1T 0H 0Z 0E 1z = 1000.1

Further examples:

1E 1h = 1E 0z 1h = 1.01

1h 5t = 0E 0z 1h 5t = 0.015

but: 0.0150 = 0E 0z 1h 5t 0zt = 0E 0z 1h 5t = 0.015

The comma in a decimal number determines the place values ​​of the digits.

There are 2 kinds of zeros in decimal fractions:

  • For missing values ​​between the highest and the lowest value have to you write zeros.
  • You can leave out ending zeros after the decimal point. The value of the number does not change.
    0.3 or 0.30 or 0.300 etc. have the same value. You write 0.3.

Other countries other manners

Period or comma?

In some countries, such as England or America, a decimal point is used instead of a decimal point: 1.5 instead of 1.5.

If you use a calculator, so be it. To type a comma, use this key with the period.

Image: iStockphoto.com (Tom Brown)

In advertisements, prices are sometimes given with a decimal point instead of a decimal point.

In your exercise book you write the decimal fractions with commas.

You may know dots in numbers from large numbers. To make it easier to read, you might write periods between groups of three digits: 1,234,567. It is better to leave small spaces in place of the dots: 1 234 567 so that you don't get confused with decimal points or commas.

Period or comma

Point numbers big numbers
Germany 1,5 1,000,000 or
1 000 000
English speaking area 1.5 1,000,000 or
1 000 000

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