Question

Which is the best estimate for (6.3 * 10⁻2)(9.9 * 10⁻3) written in scientific notation?

a. 6.3 * 10⁻5
b. 6.3 * 10⁻4
c. 6.3 * 10⁻3
d. 6.3 * 10⁻6

Answer 1

The best estimate for (6.3 × 10⁻²)(9.9 × 10⁻³) written in scientific notation is 6.3 × 10⁻µ, after multiplying the significant figures and adding the exponents.

Step-by-step explanation:

To estimate the product of (6.3 × 10⁻²)(9.9 × 10⁻³) and express it in scientific notation, we multiply the significant figures and add the exponents of the powers of 10:

Step 1: Multiply the significant figures:

• 6.3 × 9.9 ≈ 62.37 (we can round this to one significant figure, 6, because we need an estimate)

Step 2: Add the exponents:

• (10⁻²)(10⁻³) = 10⁻²⁻³ = 10⁻µ

Now, combine the significant figure with the power of 10:

6 × 10⁻µ

However, we notice that 6 is not within the standard range for scientific notation (1 to 10). Therefore, we need to adjust it:

6 × 10⁻µ = 0.6 × 10⁻´ = 6.0 × 10⁻µ (Since 0.6 is less than 1, we adjust the exponent by 1 to keep the same value).

So, the best estimate for the product in scientific notation is 6.3 × 10⁻µ, which corresponds to option a.