Question

Analyzing an Estimated Quotient
An astronomer estimated the distance from Earth to Mercury to be 5.9 × 107 miles, and the distance from Earth to Neptune to be 2.7 × 109 miles. He wanted to know how many times farther it is from Earth to Neptune than from Earth to Mercury. Consider his work.

1.
(2.7 × 109)
(5.9 × 107)

2. (
3.0
6.0
) (
109
107
)

3. 0.5 × 102

The astronomer concluded that the distance in miles from Earth to Neptune is 50 times the distance from Earth to Mercury.

Is he correct? If not, what was his mistake?
Yes, he is correct.
No, the numerator and denominator need to be switched in the expression.
No, he needed to round down in his estimation of the coefficients.
No, he needed to multiple the coefficients.

Answer 1

No. His setup and division are correct, but his rounding made the estimate too large.

(2.7 × 10^9) / (5.9 × 10^7) = (2.7/5.9) × 10^2 ≈ 0.4576 × 100 ≈ 45.8, not 50. By rounding 2.7 to 3 and 5.9 to 6 he overestimated; he should have rounded more carefully (i.e., rounded the coefficients down) to get a closer estimate.