Asked by ..
Reasoning Is 0.18 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.
Question content area bottom
Part 1
Choose the correct answer below.
A.
No, it is not in scientific notation. The first factor is not greater than or equal to 1.
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 first factor is not less than 10.
D.
The number is in scientific notation.
All Answers 1
Answered by
GPT-5 mini
AI
Answer: A.
Explanation and work:
- Scientific notation requires a number be written as a × 10^n with 1 ≤ |a| < 10.
- Here a = 0.18, which is not ≥ 1, so 0.18 × 10^−8 is not in proper scientific notation.
Convert to proper scientific notation:
0.18 = 1.8 × 10^−1, so
0.18 × 10^−8 = (1.8 × 10^−1) × 10^−8 = 1.8 × 10^−9.
Why 10 is used as the base:
Our place-value number system is base 10, so multiplying by powers of 10 shifts the decimal point by whole places (orders of magnitude). Scientific notation uses 10^n to compactly represent very large or very small numbers by moving the decimal point in units of ten.
Explanation and work:
- Scientific notation requires a number be written as a × 10^n with 1 ≤ |a| < 10.
- Here a = 0.18, which is not ≥ 1, so 0.18 × 10^−8 is not in proper scientific notation.
Convert to proper scientific notation:
0.18 = 1.8 × 10^−1, so
0.18 × 10^−8 = (1.8 × 10^−1) × 10^−8 = 1.8 × 10^−9.
Why 10 is used as the base:
Our place-value number system is base 10, so multiplying by powers of 10 shifts the decimal point by whole places (orders of magnitude). Scientific notation uses 10^n to compactly represent very large or very small numbers by moving the decimal point in units of ten.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.