Scientific Notation

Question

A company produces 4.56 x 10 to the 3rd pwer light bulbs each week. Written in scientific notatio, which is the best estimate of how many light bulbs the company will make in 9.36 x 10 to the 2nd power weeks?

Answer 1

4.56 x 10³ light bulbs per week x 9.36 x 10² weeks = (4.56 x 9.36) x (10³ x 10²) = 42.6816 x 10⁵ light bulbs = 4.26816 x 10⁶ light bulbs

 

Remember, when multiplying two exponents with the same base, the exponents add (10³ x 10² = 10²⁺³ = 10⁵)

 

Check:

 

4.56 x 10³ = 4560 light bulbs

9.36 x 10² weeks = 936 weeks

 

4560 x 936 = 4,268,160 light bulbs = 4.26816 x 10⁶

 

Answer 2

4.56 x 10³light bulbs/week ×9.36×10²weeks=4.56×9.36×10⁵light bulbs

=42.6816×10⁵light bulbs=4.27×10⁶light bulbs to 2 decimal places or

4.26816×10⁶light bulbs exactly

Answer 3

Hello,

 

9.36 x 10^2 is almost equal to 1000 (10 x 10^2 = 10^3, which is 1000).  When you multiply 10^3 by the original number, 4.56 x 10^3, you add the 2 exponents, so a good estimate would be 4.56 x 10^6 (or 4560000).  :)

Answer 4

Total bulbs produced = 4.56 x 10³ x 9.36 x 10² = 426816 x 10⁵ = 4.26 x 10¹⁰

Answer 5

If the company produces a fixed quantity of light bulbs in  a week, the number of light bulbs can be found by simply multiplying that quantity by the number of weeks.

 

4.56 * 10^3 * 9.36 * 10^2 = 42.6816 * 10^5 = 4.26816 * 10^6.

 

Rounding to the nearest hundredth,

 

The company will produce 4.27 * 10^6 light bulbs in that time period.