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Scientific Notation

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?

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Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor
4.9 4.9 (384 lesson ratings) (384)
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
 
Michael F. | Mathematics TutorMathematics Tutor
4.6 4.6 (5 lesson ratings) (5)
0
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
Amy C. | Amy C., Award-winning teacher and tutor of Science and MathAmy C., Award-winning teacher and tutor ...
5.0 5.0 (167 lesson ratings) (167)
0
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).  :)
Adam S. | Professional and Proficient Math TutorProfessional and Proficient Math Tutor
0
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.
 
 
Amarjeet K. | Professional Engineer for Math and Science TuroringProfessional Engineer for Math and Scien...
4.6 4.6 (8 lesson ratings) (8)
0
Total bulbs produced = 4.56 x 103 x 9.36 x 102 = 426816 x 105 = 4.26 x 1010