Scientific Notation Unit Review

Scientific Notation Unit Review

by Debbie Motsinger

​Scientific notation is used for very large or very small numbers using powers of 10.

​

​A number written in scientific notation is written as the product of a number between 1 & 10 (a number with only one non-zero digit before the decimal) times a power of 10.

​

​Example: 2.458 x 10¹²

Multiple Choice

Is 45.67 x 10^-2 written in correct scientific notation?

• Yes

• No

Multiple Choice

Is 1.234 x 10⁵ written in correct scientific notation?

• Yes

• No

Multiple Choice

Why is 961.2 x 10³ not correct scientific notation?

• 961.2 is not a number between 1 & 10.

• 10³ is not a power of 10.

• 961.2 x 10³ is not a product.

Fill in the Blanks

In the number 961.2 x 10³, how does 961.2 have to be written for it to be correct scientific notation?

Convert Between Scientific Notation & Standard Form​

​Convert from Scientific Notation to Standard Form.

​When a number is written in scientific notation the exponent tells you where to move the decimal.

• A POSITIVE exponent tells the decimal to move RIGHT the number of places equal to the exponent.

​Example: 3.45 x 10⁴ - move the decimal right 4 places -> 34,500

​

• ​A NEGATIVE exponent tells the decimal to move LEFT the number of places equal to the exponent.

​Example: 2.15 x 10^-5 - move the decimal left 5 places ->. 0.0000215

Multiple Choice

Write 2.4 x 10⁵ in standard form.

• 2,400,000

• 240,000

• 0.000024

• 0.0000024

Multiple Choice

Write 1.057 x 10^-3 in standard form.

• 1057

• 0.001057

• -1057

• -0.001057

Convert from standard form to scientific notation.​

• ​rewrite the number so that it only has one digit before the decimal

• ​multiply the new number x a power of ten

• ​the exponent is equal to the number of places the decimal moved

  • ​If the decimal moved to the RIGHT the exponent will be NEGATIVE.

​EXAMPLE: 0.00023 = 2.3 x 10^-4

​

• ​If the decimal moved to the LEFT the exponent will be POSITIVE.

​Example: 7,750,000 = 7.75 x 10 ⁶

Multiple Choice

Write 2,345,000 in scientific notation.

• 2.345 x 10^-6

• 2.345 x 10⁶

• 23.45 x 10^-5

• 23.45 x 10⁵

Multiple Choice

Write 0.0135 in scientific notation.

• 1.35 x 10^-2

• 1.35 x 10²

• 0.135 x 10^-1

• 13.5 x 10²

How to Compare and Order Numbers in Scientific Notation​

​Comparing & ordering when the powers are the same.

• ​Only the decimal number must be compared

​

​Example: 6.78 x 10⁴ ___ 5.92 x 10⁴

​

• ​The powers of 10 are the same.

• Only compare 6.78 and 5.92.

• 6.78 > 5.92 therefore 6.78 x 10⁴ > 5.92 x 10⁴.

Multiple Choice

4.25 x 10² ___ 3.19 x 10²

• <

• >

• =

Multiple Choice

7.12 x 10^-4 ___ 2.17 x 10^-4

• <

• >

• =

Multiple Choice

Order the following from LEAST to GREATEST.

3.21 x 10⁴, 3.201 x 10⁴, 3.021 x 10⁴

• 3.21 x 10⁴

  3.201 x 10⁴

  3.021 x 10⁴

• 3.21 x 10⁴

  3.021 x 10⁴

  3.201 x 10⁴

• 3.201 x 10⁴

  3.021 x 10⁴

  3.21 x 10⁴

• 3.021 x 10⁴

  3.201 x 10⁴

  3.21 x 10⁴

Comparing and ordering if the ​POWERS are DIFFERENT

• Only the exponents must be compared - the greater exponent is the greater number.

​

​Example: 9.875 x 10⁴ _____ 8.456 x 10³

• ​The powers of 10 are different

• ​Compare the exponents

• ​4 > 3 therefore 9.875 x 10⁴ > 8.456 x 10³.

​Adding Numbers in Scientific Notation

​1. To add and subtract numbers in scientific notation, the numbers must have the same exponent.

​2. Use LARS (Left Add Right Subtract) to help you rewrite the numbers.

​3. Rewrite one of the numbers to have the same exponent as the other.

​4. Add the decimal numbers and the power of ten does not change.

​5. Make sure the answer is in correct scientific notation - use LARS to correct if needed.

​

​Example: 2.3 x 10⁴ + 1.5 x 10³. Let's rewrite the second number.

​ 2.3 x 10⁴ + .15 x 10⁴. Since 1 is added to the exponent, move the decimal left 1.

​ (2.3 + .15) x 10⁴ Add the decimal numbers and the power of 10 stays the same.

​ 2.45 x 10⁴

Multiple Choice

1.234 x 10² + 5.67 x 10³

• 57.934 x 10²

• 5.7934 x 10³

• 6.904 x 10²

• 6.904 x 10³

Multiple Choice

6.54 x 10³ _____4.65 x 10⁸

• <

• >

• =

Multiple Choice

Order the following from LEAST to GREATEST.

7.65 x 10³, 2.14 x 10⁹, 9.25 x 10⁶

• 2.14 x 10⁹

  7.65 x 10³

  9.25 x 10⁶

• 9.25 x 10⁶

  7.65 x 10³

  2.14 x 10⁹

• 7.65 x 10³

  9.25 x 10⁶

  2.14 x 10⁹

• 7.65 x 10³

  2.14 x 10⁹

  9.25 x 10⁶