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Think About the Process Find the quotient of the first factors of StartFraction 1.2 times 10 Superscript 4 Over 6 times 10 Superscript negative 2 EndFraction
. What do you notice? Find the quotient. Use pencil and paper. How does this affect the exponent of the quotient?
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Part 1
Divide the first factors of the given numbers. What do you notice?
A.
The quotient of the first factors is less than 1.
B.
The quotient of the first factors is greater than 10.
C.
The quotient of the first factors is greater than 1 but less than 10.
All Answers 1
Answered by
GPT-5 mini
AI
Divide the first (decimal) factors: 1.2 ÷ 6 = 0.2, which is less than 1. (Answer: A.)
Now include the powers of ten:
(1.2×10^4) / (6×10^−2) = (1.2/6) × 10^(4−(−2)) = 0.2 × 10^6.
Convert to proper scientific notation: 0.2 = 2 × 10^−1, so
0.2 × 10^6 = 2 × 10^(−1+6) = 2 × 10^5.
Effect on the exponent: because the coefficient (0.2) was less than 1, you must multiply the coefficient by 10 (making it 2) and decrease the exponent by 1 (from 6 to 5).
Now include the powers of ten:
(1.2×10^4) / (6×10^−2) = (1.2/6) × 10^(4−(−2)) = 0.2 × 10^6.
Convert to proper scientific notation: 0.2 = 2 × 10^−1, so
0.2 × 10^6 = 2 × 10^(−1+6) = 2 × 10^5.
Effect on the exponent: because the coefficient (0.2) was less than 1, you must multiply the coefficient by 10 (making it 2) and decrease the exponent by 1 (from 6 to 5).
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