Asked by jayy
Reasoning Is 7.63 times 22 Superscript 6 in scientific notation? If not, explain. Use pencil and paper. Explain why 10 is used as the base in the second scientific notation factor.
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Part 1
Choose the correct answer below.
A.
No, it is not in scientific notation. The first factor is not less than 10.
B.
No, it is not in scientific notation. The second factor is not a power of 10.
C.
No, it is not in scientific notation. The first factor is not greater than or equal to 1.
D.
The number is in scientific notation.
All Answers 1
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GPT-5 mini
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Answer: B.
Reason: Scientific notation must be written as a × 10^n with 1 ≤ a < 10 and n an integer. In 7.63 × 22^6 the first factor 7.63 satisfies 1 ≤ 7.63 < 10, but the second factor 22^6 is not a power of 10, so the expression is not in scientific notation.
Why base 10? Because our decimal system uses base 10, so multiplying by 10^n shifts the decimal point n places. That makes the exponent directly count decimal-place shifts and gives a unique, convenient standard form. For example 7.63 × 10^6 = 7,630,000 (move the decimal 6 places right).
(If you want to rewrite 7.63×22^6 in proper scientific notation, compute 22^6 = 113,379,904, then 7.63×113,379,904 = 865,088,667.52 ≈ 8.6508866752×10^8.)
Reason: Scientific notation must be written as a × 10^n with 1 ≤ a < 10 and n an integer. In 7.63 × 22^6 the first factor 7.63 satisfies 1 ≤ 7.63 < 10, but the second factor 22^6 is not a power of 10, so the expression is not in scientific notation.
Why base 10? Because our decimal system uses base 10, so multiplying by 10^n shifts the decimal point n places. That makes the exponent directly count decimal-place shifts and gives a unique, convenient standard form. For example 7.63 × 10^6 = 7,630,000 (move the decimal 6 places right).
(If you want to rewrite 7.63×22^6 in proper scientific notation, compute 22^6 = 113,379,904, then 7.63×113,379,904 = 865,088,667.52 ≈ 8.6508866752×10^8.)
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