Question

practice question - chapter 0 (toolbox)
2b. what is the longest length?
(a) $10^{-2}$ km
(b) 1 m
(c) 100 mm
(d) $10^7$ nm
work!

Explanation:

Step1: Convert all units to the same system (e.g., meters)

• Option A: \(10^{-2}\text{ km}\). Since \(1\text{ km} = 1000\text{ m}\), \(10^{-2}\text{ km}=10^{-2}\times1000\text{ m}=10\text{ m}\).
• Option B: \(1\text{ m}\).
• Option C: \(100\text{ mm}\). Since \(1\text{ m}=1000\text{ mm}\), \(100\text{ mm}=\frac{100}{1000}\text{ m}=0.1\text{ m}\).
• Option D: \(10^{7}\text{ nm}\). Since \(1\text{ m}=10^{9}\text{ nm}\), \(10^{7}\text{ nm}=\frac{10^{7}}{10^{9}}\text{ m}=0.01\text{ m}\).

Step2: Compare the converted lengths

Compare \(10\text{ m}\) (Option A), \(1\text{ m}\) (Option B), \(0.1\text{ m}\) (Option C), and \(0.01\text{ m}\) (Option D). The largest value is \(10\text{ m}\) (from Option A).

Answer:

A. \(10^{-2}\text{ km}\)