Question

Multiply (9 x 10^5) · (9 x 10^7).

A. 8.1 x 10^12
B. 9 x 10^12
C. 8.1 x 10^13
D. 9 x 10^13

Option 1: A
Option 2: B
Option 3: C
Option 4: D

Answer 1

To multiply (9 x 10^5) and (9 x 10^7) in scientific notation, multiply the base numbers (9 x 9) and add the exponents (5+7), resulting in 8.1 x 10^13.

Step-by-step explanation:

The student is asking how to multiply two numbers expressed in scientific notation: (9 x 105) and (9 x 107). Multiplying numbers in scientific notation involves multiplying the base numbers and adding the exponents of the powers of ten. First, we multiply the base numbers: 9 x 9 = 81. Then, we add the exponents: 5 + 7 = 12.

Since 81 is not between 1 and 10, we need to adjust it to fit proper scientific notation. We express 81 as 8.1 x 10, which introduces another power of ten. Therefore, the multiplication results in 8.1 x 10 (base numbers) times 1012 (sum of exponents), or 8.1 x 1013.