Scientific notation is a compact way of writing very large or very small numbers. A number written in scientific notation follows the form a×10b where 1≤a<10 and b is an integer. For example, the number 4 million can be rewritten as the product of 4 and a multiple of 10. Then, the multiple of 10 is rewritten as a base 10 power. 4000000=4×1000000=4×106 Scientific notation can also be applied to very small decimal numbers, where there are many zeros before the significant digits, such as 0.000342. 0.000342=3.42÷10000=3.42×10-4 In such cases, numbers are rewritten as a division by a multiple of 10. Division by a multiple of 10 is equivalent to multiplication by a base 10 power with negative exponent. Below are a few more examples of numbers written in scientific notation.
Decimal Form | Write as a product or division | Scientific Notation |
---|---|---|
4505 | 4.505×1000 | 4.505×103 |
8320000 | 8.32×1000000 | 8.32×106 |
0.0005 | 5÷10000 | 5×10-4 |
0.0521 | 5.21÷100 | 5.21×10-2 |
An intuitive way to rewrite a number greater than 10 in scientific notation is done by counting the number of places the decimal needs to move
so the number is greater than or equal to 1 and less than 10. The number of places the decimal moved from right to left indicates the exponent to be used for the base 10 power.
Similarly, for numbers less than 1, such as 0.000022, the decimal will move
from left to right. In this case, the number of places moved indicates the negative exponent to be used for the base 10 power.