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Reasoning Is 25 times 10 Superscript 0 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 number is not written as a product of 2 factors.
C.
No, it is not in scientific notation. The second factor is not a power of 10.
D.
The number is in scientific notation.
All Answers 1
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Answer: A.
Reasoning (work shown):
- 25 × 10^0 = 25 × 1 = 25.
- Scientific notation requires a × 10^n with 1 ≤ |a| < 10 and n an integer.
- Here the first factor a = 25, which is not less than 10, so this is not in proper scientific notation.
You can rewrite it correctly:
25 × 10^0 = 2.5 × 10 × 10^0 = 2.5 × 10^1,
and now 2.5 satisfies 1 ≤ 2.5 < 10.
Why base 10? Because we use the decimal (base‑10) number system. Multiplying or dividing by powers of 10 shifts the decimal point, which is exactly what scientific notation uses to separate a number into a coefficient between 1 and 10 and an appropriate power-of-10 factor.
Reasoning (work shown):
- 25 × 10^0 = 25 × 1 = 25.
- Scientific notation requires a × 10^n with 1 ≤ |a| < 10 and n an integer.
- Here the first factor a = 25, which is not less than 10, so this is not in proper scientific notation.
You can rewrite it correctly:
25 × 10^0 = 2.5 × 10 × 10^0 = 2.5 × 10^1,
and now 2.5 satisfies 1 ≤ 2.5 < 10.
Why base 10? Because we use the decimal (base‑10) number system. Multiplying or dividing by powers of 10 shifts the decimal point, which is exactly what scientific notation uses to separate a number into a coefficient between 1 and 10 and an appropriate power-of-10 factor.
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