< 1 >
Decimal numeral system
The decimal system uses the ten numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 for writing decimal numbers.
Explanation
The number 237 is composed of
2 × 100 = 2 × 102
3 × 10 = 3 × 101
7 × 1 = 7 × 100
You know that 100 is equal to 10 × 10 = 102 and you can write a 10 as 101, and a 1 like 100. If there are digits after decimal point this continues. The power decreases, reaches less than zero, which means it becomes negative. Thus 0,1 = 10–1. The number 4267,893 is composed of
4 × 1000 = 2 × 103
2 × 100 = 2 × 102
6 × 10 = 6 × 101
7 × 1 = 7 × 100
8 × 0,1 = 8 × 10−1
9 × 0,01 = 9 × 10−2
3 × 0,001 = 3 × 10−3
Behind every digit in a number is a power of 10, that depends on its position. Because of that you must write a 0 if a certain place has no value. The number 3600,102 is composed of
3 × 1000 = 3 × 103
6 × 100 = 6 × 102
1 × 0,1 = 1 × 10−1
2 × 0,001 = 2 × 10−3
Now we understand why is
And we better understand the number 1, as
We have seen that numbers with a negative exponent are just fractions. You see it clearly in