Question

Reasoning  Is 6.62 times 26 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 first factor is not greater than or equal to 1.
C.
​No, it is not in scientific notation. The second factor is not a power of 10.
D.
The number is in scientific notation.

Answer 1

Correct choice: C.

Explanation and work (by hand):

Scientific notation requires a number written as a × 10^n with 1 ≤ a < 10 and n an integer. The given expression 6.62 × 26^6 has the correct first factor 6.62 (it is between 1 and 10), but the second factor 26^6 is not a power of 10, so it is not in scientific notation.

You can rewrite it to scientific notation by moving the factor 10 out of 26:
26 = 2.6 × 10, so
26^6 = (2.6 × 10)^6 = 2.6^6 × 10^6.

Thus
6.62 × 26^6 = 6.62 × 2.6^6 × 10^6.

Compute 2.6^6 ≈ 308.915776, so
6.62 × 2.6^6 ≈ 6.62 × 308.915776 ≈ 2045.05.

So the product ≈ 2045.05 × 10^6 = 2.04505 × 10^3 × 10^6 = 2.04505 × 10^9.

Therefore the expression is not originally in scientific notation (option C); in scientific notation it is about 2.04505 × 10^9.

Why base 10? Because our place-value (decimal) system uses base 10: multiplying or dividing by 10 shifts the decimal point one place, so powers of 10 conveniently record how many places the decimal point is moved. That is why scientific notation uses 10 as the base.