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 × 10*^{8} and the population of the world as
7 × 10^{9}, and determine that the world population is more than 20 times larger.

Common Core: 8.EE.3

### Suggested Learning Targets

** 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 10^{7} miles away, and Planet B is 3 x 10^{4} 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 10^{4}

3.2 x 10^{12}
1.55 x 10^{6}
**Negative Scientific Notation**

**Ordering Numbers in Scientific Notation**

Example:

Order from Least to Greatest

0,052 x 10^{7}, 5.2 x 10^{5}, 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 10^{7}, 5300 x 10^{-1}, 5.3 x 10^{5}, 530 x 10^{8}
**Compare numbers in scientific notation**

Example:

How much greater is:

6 x 10^{5} than 2 x 10^{3}

8.4 x 10^{9} than 2.1 x 10^{8}
**Scientific Notation**

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

- 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.

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 10

Examples:

Change these numbers into scientific notation.

56,900,000

267,000

46,205,000

Change these numbers into standard form

5.07 x 10

3.2 x 10

Example:

Order from Least to Greatest

0,052 x 10

9 x 10

50.1 x 10

0.53 x 10

Example:

How much greater is:

6 x 10

8.4 x 10

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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