Multiplying and Dividing with Scientific Notation

Multiplying and Dividing with Scientific Notation

By Wendolyn Gildehaus

Multiple Choice

10⁵ x 10³ =

• 10¹⁵

• 10²

• 10⁸

• 10

Have a calculator (chromebook) handy!!

​Some text here about the topic of discussion.

Multiplying with Scientific notation

​Rearrange and use exponent rules

​To multiply values in scientific notation, rearrange the multiplication problem and apply the rules of exponents.

​

For example (4.5 x 10⁵) (2 x 10³) = ( 4.5 x 2 )( 10⁵ x 10³ )​

Therefore, the final answer​ in scientific notation would be: 9 x 10⁸

​

Multiple Choice

(1.5 x 10⁵) (5 x 10³) =

• 75 x 10⁸

• 7.5 x 10⁸

• 75 x 10¹⁵

• 7.5 x 10¹⁵

Multiple Choice

(1.5 x 10⁵) (5 x 10³) = in standard form

• 75000000

• 750000000

• 75000000000000000

• 7500

only one digit before the decimal

What happens when you try

​(3 x 10⁴) (7.2 x 10²) = and get (3 x 7.2)( 10⁴ x 10²) = 21.6 x 10⁶

21 is not one digit. uh oh.

We have to move the decimal point one space to the left - BUT THAT AFFECTS THE 10⁶ TOO!! ​

Subject | Subject

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Multiple Choice

​ 21.6 x 10⁶ =

• 2.16 x 10⁶

• 2.16 x 10⁵

• 2.16 x 10⁷

​That's right...

​

​(3 x 10⁴) (7.2 x 10²) = and get (3 x 7.2)( 10⁴ x 10²) = 21.6 x 10⁶

​

and 21.6 x 10⁶ = 2.16 x 10⁷

​

If we move the decimal to make the number smaller, then we compensate by making the power of ten bigger by that many moves!​

Subject | Subject

Some text here about the topic of discussion

Multiple Choice

​(3 x 10⁴) (7.2 x 10²) = in standard form?

• 21600000

• 2160000

• 216000

• 216000000

Multiple Choice

10⁶

10³

• 10⁹

• 10²

• 10^-3

• 10³

Dividing with scientific notation

​rearrange the division problem and apply the rules of exponents

For example, (8 x 10⁶) = (8) x (10⁶ )

​ (4 x 10³) (4) x (10³ )

​

= 2 x 10³

​

​

Some text here about the topic of discussion

have you noticed these are the answers???

​You should probably be writing this on your paper I will be grading.....

Multiple Choice

9 x 10⁹

3 x 10⁷

In Scientific Notation (one digit before the decimal point)

• 3 x 10²

• 3 x 10³

• 3 x 10¹⁶

• 3 x $$10^1$$

Multiple Choice

9 x 10⁹

3 x 10⁷

In Standard Form.....

• 300

• 3

• 3000

• 30

Multiple Choice

9.45 x 10⁷

2.1 x 10²

In Scientific Notation....

• 4.5 x 10

• 4.5 x 10⁵

• 4.5 x 10⁹

• 4.5 x 10^3.5

Multiple Choice

9.45 x 10⁷

2.1 x 10²

In Standard Form

• 4500000

• 450000

• 45000

• 45000000