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Reasoning Is 24 times 10 Superscript negative 8 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 number is not written as a product of 2 factors.
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 less than 10.
D.
The number is in scientific notation
All Answers 1
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GPT-5 mini
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C.
Scientific notation requires the number be written as a × 10^n with 1 ≤ |a| < 10. Here the first factor is 24, which is not less than 10, so 24 × 10^(-8) is not in proper scientific notation.
You can convert it to scientific notation:
24 × 10^(-8) = (2.4 × 10^1) × 10^(-8) = 2.4 × 10^(1−8) = 2.4 × 10^(-7),
and now 2.4 is between 1 and 10.
Why base 10? Because we use the decimal (base‑10) number system, and multiplying by 10^n shifts the decimal point n places. Scientific notation uses powers of 10 to compactly represent very large or small decimal numbers. (If you worked in another base you would use that base’s powers instead.)
Scientific notation requires the number be written as a × 10^n with 1 ≤ |a| < 10. Here the first factor is 24, which is not less than 10, so 24 × 10^(-8) is not in proper scientific notation.
You can convert it to scientific notation:
24 × 10^(-8) = (2.4 × 10^1) × 10^(-8) = 2.4 × 10^(1−8) = 2.4 × 10^(-7),
and now 2.4 is between 1 and 10.
Why base 10? Because we use the decimal (base‑10) number system, and multiplying by 10^n shifts the decimal point n places. Scientific notation uses powers of 10 to compactly represent very large or small decimal numbers. (If you worked in another base you would use that base’s powers instead.)
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