 # Scientific Notation

Solutions, examples, videos, and lessons to help Grade 8 students learn to how to use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.
For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger.

Common Core: 8.EE.3

### Suggested Learning Targets

• I can express numbers as a single digit times an integer power of 10 (Scientific Notation).
• I can use scientific notation to estimate very large and/or very small quantities.
• I can compare quantities to express how much larger one is compared to the other.
The following figures show how to convert to scientific notation. Scroll down the page for examples and solutions. Estimating Using Scientific Notation (8.EE.3)
Scientific Notation for Large Numbers.
Scientific Notation for Small Numbers.
Comparing Numbers.
Example:
The planet Lukon has 2 neighboring planets. Planet A is 9 x 107 miles away, and Planet B is 3 x 104 miles away. How many times further away is Planet A than Planet B? Positive Scientific Notation
Examples:
Change these numbers into scientific notation.
56,900,000
267,000
46,205,000
Change these numbers into standard form
5.07 x 104
3.2 x 1012 1.55 x 106 Negative Scientific Notation

Ordering Numbers in Scientific Notation
Example:
Order from Least to Greatest
0,052 x 107, 5.2 x 105, 53.2 x 10, 534
9 x 10-7, 8 x 10-8, 7 x 10-6, 6 x 10-10
50.1 x 10-3, 4.8 x 10-1, 0.52 x 10-3, 56 x 10-2
0.53 x 107, 5300 x 10-1, 5.3 x 105, 530 x 108 Compare numbers in scientific notation
Example:
How much greater is:
6 x 105 than 2 x 103
8.4 x 109 than 2.1 x 108 Scientific Notation

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