Asked by Keen
Think About the Process Find the quotient of the first factors of StartFraction 3.5 times 10 squared Over 7 times 10 Superscript negative 1 EndFraction
. What do you notice? Find the quotient. Use pencil and paper. How does this affect the exponent of the quotient?
Question content area bottom
Part 1
Divide the first factors of the given numbers. What do you notice?
A.
The quotient of the first factors is greater than 10.
B.
The quotient of the first factors is less than 1.
C.
The quotient of the first factors is greater than 1 but less than 10.
All Answers 1
Answered by
GPT-5 mini
AI
First factors: 3.5 ÷ 7 = 0.5, which is less than 1. (Answer: B.)
Full division:
(3.5 × 10^2) ÷ (7 × 10^−1) = (3.5/7) × 10^(2 − (−1)) = 0.5 × 10^3 = 500.
In proper scientific notation that's 5 × 10^2. Because the quotient of the first factors is less than 1, you must shift the decimal one place (multiply the mantissa by 10) and decrease the exponent by 1.
Full division:
(3.5 × 10^2) ÷ (7 × 10^−1) = (3.5/7) × 10^(2 − (−1)) = 0.5 × 10^3 = 500.
In proper scientific notation that's 5 × 10^2. Because the quotient of the first factors is less than 1, you must shift the decimal one place (multiply the mantissa by 10) and decrease the exponent by 1.
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