Official Guide Explanation:
Problem Solving #28




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Solution and Metadata

Question: 28
Page: 156
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Measurement Problems >

Explanation: This is a tricky measurement question, but you can solve it with the same techniques you'd use on any question involve unit conversion. We're told that 1 kilometer is the same as 3.9 * 104 inches. All we need to do is use that conversion to turn 2.3 * 1014 inches into kilometers.

To do so, we'll multiply that distance by 1. Since 1 km is the same as 3.9 * 104 inches, a fraction with one of those in the numerator and the other in the denominator equals 1. Our math should look like this:

2.3 * 1014 inches * ((1\text{ km})/(3.9 * 104\text{ inches}))

The "inches" cancel out, so we're left with:

((2.3 * 1014)/(3.9 * 104))km

To simplify, first deal with the exponents:

((2.3)/(3.9)) * ((1014)/(104)) = ((2.3)/(3.9)) * 1010

((2.3)/(3.9)) is about the same as (24/40), or 0.6, so we can approximate as:

0.6 * 1010

= 6 * 109, which is very close to choice (B).

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