The calculator works as follows:
The calculator works as follows:
A decimal number, like a fraction, indicates the part of a whole.
Fractions and decimals can be converted to each other.
Not all fractions can be written as a fraction with a power of 10 in the denominator.
The fraction 1/3 is an example of this.
In such a case it is always possible to calculate the decimal number using long division.
With long division you can find the decimal number of any fraction.
Example 1: The Fraction 3/88 | / | 3 | 0 | 0 | 0 | \ | 0,375 |
0 | |||||||
3 | 0 | ||||||
2 | 4 | ||||||
6 | 0 | ||||||
5 | 6 | ||||||
4 | 0 | ||||||
4 | 0 | ||||||
0 |
The long division stops here because the remainder becomes 0.
If the remainder is 0 then the decimal number is exactly equal to the fraction.
Dus: 3/8 = 0,375
3 | / | 1 | 0 | 0 | 0 | 0 | 0 | \ | 0,33333 |
0 | |||||||||
1 | 0 | ||||||||
9 | |||||||||
1 | 0 | ||||||||
9 | |||||||||
1 | 0 | ||||||||
9 | |||||||||
1 | 0 | ||||||||
9 | |||||||||
1 | 0 | ||||||||
9 | |||||||||
1 |
It does not matter how long you continue with long division,
The remainder always remains 1 and the next number after the decimal point is always 3.
The decimal number 0.33333 is therefore only an approximation of the fraction 1/3.
The decimal number 0.3333333333 is a more accurate approximation, with 10 decimal places.
The numbers after the decimal point are also called decimals.