 WME@Kimpton Middle

## Scientific Notation In astronomy, distances are huge and usually measured in light years. One light year is the distance light travels in a year. The diagram on the right shows one light year to be approximately

9.15 × 1012 = 9.15E12

The notation 1012 means multiplying 12 tens together. Here, the number 10 is the base and the number 12 is the exponent. And the number is the 10 to the power 12.

The exponent tells you how many bases to multiply together.

A power of 10:    103 = 10 ×10 ×10 = 1000
A power of 2:    24 = 2×2 ×2×2 = 16

1. Experiment with different bases and exponents using this tool.

=   ?

2. See what happens if you set the base to a negative number.

3. See what happens if you set the base to zero.

4. See what happens if you set the exponent to zero.

5. If a negative exponent is given, then it simply means a fraction one over the number with the exponent turned positive. For example,

10− 6 = 1 / 106 = 0.000001
2− 3 = 1 / 23 = 1 / 8

In the tool above, try some negative powers.

### Converting to Scientific Notation

A number is in scientific notation if it is written as the product of a number whose absolute value is between 0 and 10 multiplied by a power of 10. For example, 213 = 2.13 × 102 (2.13E2) and 0.0003 = 3 × 10-4 (3E-4).

Here is the rules to remember:

• When you multiply a number by 10, you move the decimal point to the right by one place.

• When you multiply a number by 10-1, you move the decimal point to the left by one place.

Write these numbers in scientific notation.

• 158.23 =  × 10

• 0.187 =  × 10