# Why are fractions not referred to as percentages

### How do you measure chance?

You have already measured a lot.

**Lengths**

To measure a distance, put a tape measure on the distance. The units are on the tape measure. For example, you read 2 m.

**Filling quantities**

At the Oktoberfest in Bavaria there are beer mugs. They hold a liter of liquid. Here the number of measurements serves as an indication of the number of full jugs.

**Random experiments**

In a random experiment, the outcomes can have different probabilities. That is why there is also a measure here to measure how likely the outcome is. Each result of a random experiment is assigned a number that should indicate how likely it is that the result will occur.

The good thing is, there are limits to this measure. There can only be numbers between 0 and 1.

If one assigns the probability of occurrence to each result of a random experiment, this is called the measure of probability.

### Why is the measure between 0 and 1?

**Handing out gifts**

Lisa and Quan are class representatives of the 7a. In the last hour before the Christmas holidays, all pupils should bring a present for a drawn pupil. So that everything happens randomly, Lisa and Quan have written all the names of the students on a piece of paper. One after the other, all students draw a name. At the end of the drawing, all students will be distributed.

There is no case that a student has drawn a name from another class. This is not possible. Therefore the probability is 0% here. All students are distributed. That said, everyone has certainly come up with a name. So the probability is 100% of receiving a gift.

**roll the dice**

Each time the die is rolled, a number between 1 and 6 appears. You can never roll the 7.

Thus in 100% of the cases a number between 1 and 6 appears and in 0% of the cases (never) a 7.

The probability of the outcome of a random experiment is called the individual probability. In every random experiment, the sum of the individual probabilities results in 100%.

Remember: $$ 0% = \ frac 0 100 = 0 $$ and $$ 100% = \ frac 100 100 = 1 $$.

The probabilities of a random experiment can be plotted on a pie chart like pieces of cake. A whole cake is 100%.

### Percentages, fractions, decimals?

In the calculation of probability, one uses not only percentages for the specification of the individual probabilities. These are also converted into fractions or decimal numbers.

You already know that from the percentage calculation.

Example: $$ 1/2 = 0.5 = 50 $$ $$% $$.

**roll the dice**

The probability of rolling a 1 applies in one of 6 cases. That is, the probability measure is $$ 1/6 $$. This corresponds to the decimal number $$ 0.1 \ bar 6 $$ or $$ 16, \ bar 6% $$.

As you can see, you only avoid a periodic number in the fractions.

The individual probabilities can be specified as a fraction, percentage or decimal number. Depending on the random attempt, one representation is better than the other.

$$1/5=0,2=20$$ $$%$$

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### Decimal to fraction

For simple non-periodic decimal numbers, you count the digits after the decimal point. Now you write the decimal number without 0, as a numerator of the fraction. In the denominator you now add a 1 and add a 0 to the digits counted.

**Example:** From $$ 0.25 $$ to $$ \ frac 1 4 $$

$$0,25$$ | The number has 2 decimal places. | 1. Counting |

$$ \ frac 25 $$ | Add the number to 25 in the numerator | 2. Write counter |

$$ \ frac 25 100 $$ | Complete 1 with two zeros in the denominator | 3. Complete denominator |

$$ \ frac {25:25} {100: 25} $$ | Don't forget to shorten | 4. Shorten |

$$ \ frac 1 4 $$ | Finished! | 5. Result |

### Decimal number as percentage

To get from a decimal number to a percentage, move the decimal point of the decimal number by 2 places to the right. If a digit is missing there, you add a zero. Put the% after it.

**Example:** 0,3 = 30%

0,3 0 | Complete the 0 |

030 , | Move the comma |

30 % | Don't forget the percent sign |

**Example:** 0,455=45,5%

0,455 | No additions necessary |

045 , 5 | Move the comma |

45,5 % | Don't forget the percent sign |

### Fractional number to decimal number

You expand the fraction until you get to 10, 100, 1000, etc. in the denominator. Put a 0 and a comma in front of the counter and write the digits of the counter after it.

**Example:** $$ \ frac 1 5 = 0.2 $$

$$ \ frac {1 cdot 2} {5 \ cdot 2} $$ | extend to 10ths |

$$ \ frac 2 10 $$ | to calculate |

0, 2 | Write 0 and add counter |

$$ \ frac 1 5 $$ is the same as $$ 0.2 $$.

You can convert the number $$ 0.2 $$ to 20%.

The calculator can convert fractions to decimal numbers by tapping the b / c key or the S <=> D key. But this is different for the pocket calculator.

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