# SCIENTIFIC NOTATION

## Definition

A way to express a very large or very small number as the product of a number between 1 and 10 and a power of 10.

## Examples:

- The number 370,00,000 can be written as 3.7 x 10^8.
- The number 0.00000045 can be written as 4.5 x 10^-7.

## But how?

Think about the number 600.

- We know 600 = 6 x 100,
- and that 100 = 10^2,
- Therefore, 600 = 6 x 10^2.

## IMPORTANT

When your number is smaller than one, then your exponent should be negative.

If the number is bigger than one, then your exponent is positive.

This is important because this decides which direction you move the decimal.

## Standard 8.EEI.3

Explore the relationship between quantities in decimal and scientific notation.

a. Express very large and very small quantities in scientific notation in the form a x 10^b = p where 1<= a < 10 and b is an integer.

b. Translate between decimal notation and scientific notation.

c. Estimate and compare the relative size of two quantities in scientific notation.