Operations with Scientific Notation

operations with scientific notation

By Susan Kahler

Multiple Choice

What is scientific notation?

• A long way to write really short  numbers
• A short way to write really long numbers
• I don't know...
• None of the above

Multiple Choice

How would you write 564,000,000 in scientific notation?

• 5.64 x 10^-7
• 5.64 x 10⁶
• 5.64 x 10⁸
• 56.4 x 10⁷

Multiple Choice

How would you write 0.0005 in scientific notation?

• 5 x 10^-5
• 5 x 10^-4
• 5 x 10^-3
• .5 x 10³

Multiple Choice

How would you write -5.6 x 10^-3 in standard form?

• 0.0056
• -5,600
• 0.00056
• -0.0056

Multiple Choice

Write 9,000,000,000 in scientific notation.

• 9 x 10¹⁰

• 9 x 10⁹

• 9 x 10⁸

• 9 x 10⁷

Multiple Choice

Write 1.09 x 10^-4 in standard notation.

• 1,090

• 10,900

• 0.000109

• 0.0109

Multiple Choice

Add: remember as long as the exponents are the same you just add the first two numbers and keep 10^-5

(2 x 10^-5)+ (7 x 10^-5)

• 9 x 10^-10
• 14 x 10^-5
• 9 x 10^-5
• 1.4 x 10^-4

Multiple Choice

ADD

(8 x 10⁴) + (4 x 10⁴)

• 12 x 10⁴
• 1.2 x 10⁵
• 1.2 x 10⁹
• 1.2 x 10⁸

Multiple Choice

Write the answer in scientific notation.
7.3 x 10⁵  +   3.7 x 10⁵  =

• 11.0 x 10⁵
• 1.1 x 10¹⁰
• 1.10 x 10¹¹
• 1.1 x 10 ⁶

Multiple Choice

Subtract: Remember this is the same rule as adding.

(5 x 10⁶) - (3 x 10⁶)

• 2 x 10¹²
• 2 x 10⁶
• 2 x 1036
• 2 x 10⁰

Multiple Choice

Write the answer in scientific notation.
5 x 10⁸ -   3.4 x 10⁸  =

• 2.4 x 10⁸
• 2.4 x 10⁰
• 1.6 x 10⁰
• 1.6 x 10⁸

Multiple Choice

Write the answer in scientific notation.

When the exponents are different you have to make them match. SO for the one below subtract one from the six and move the decimal so they match.

4.1 x 10⁵ + 5.5 x 10⁶ = $$4.1\times10^5+.55\times10^5$$  =4.65 x 10⁵

• 5.91 x 10⁶

• 9.6 x 10⁵

• 9.6 x 10¹¹

• 4.65 x 10⁵

Multiple Choice

Find the difference. Use the same rule as on the slide before to make the exponents match

(3.8 x 10⁴) - (2 x 10³)

• 1.8 x 10⁴

• 1.8 x 10¹

• 3.6 x 10¹

• 3.6 x 10⁴

Multiple Choice

Subtract.

Write the answer in scientific notation.

(5 x 10⁶) - (3 x 10⁵)

• 2 x 10¹

• 4.7 x 10⁶

• 2 x 10⁶

• 47 x 10⁵

Multiple Choice

Multiply: For this you need to use the product rule. Multiply the numbers and add the exponents.

(3.4 x 10⁵)(1.2 x 10^-3)

• 4.08 x 10^-8
• 4.8 x 10²
• 4.08 x 10²
• 4.08 x 10^-15

Multiple Choice

(5 x 10⁶)(5 x 10⁷)

• 2.5 x 10¹²
• 2.5 x 10¹⁴
• 25 x 10¹²
• 25 x 10¹³

Multiple Choice

A rectangular section of land made up of wheat farms has a length of 5 X 10⁴ meters and a width of 6 X 10³ meters What is the area of the land in square meters?

• 3 X 10⁶ m²

• 3 X 10⁷ m²

• 3 X 10⁸ m²

• 3 X 10¹² m²

Multiple Choice

Multiply.

Write the answer in scientific notation.

(2 x 10⁹)(4 x 10⁴)

• 8 x 10⁵

• 6 x 10¹³

• 8 x 10¹³

• 8 x 10³⁶

Multiple Choice

Divide:
(6.9 x 10⁷) / (2.3 x 10^-3)

• 3 x 10¹⁰
• 3 x 10⁴
• 3 x 10^-4
• 3 x 10^-11

Multiple Choice

Divide: remember the fraction bar tells you to divide always. Top divided by bottom. For this you use the quotient rule, divide the numbers and subtract the exponents.

5 x 10¹² ------------ 2 x 10⁶

• 2.5 x 10²
• 2.5 x 10⁶
• 3 x 10²
• 2.5 x 10¹⁸

Multiple Choice

2 x 10⁵
----------
8 x 10²

• 2.5 x 10⁴
• 2.5 x 10²
• 25 x 10³
• .25 x 10³

Multiple Choice

Divide.

Write the answer in scientific notation.

6 x 10⁶

------------

2 x 10³

• 12 x 10³

• 3 x 10⁹

• 4 x 10³

• 3 x 10³