Question

Compare the quantities in each pair.

A. 10 m vs. 107 µm
B. 10 cL vs. (10^{-24}) C
C. 104 g vs. 10 kg
D. (10^5) ns vs. (10^2) ms

Answer 1

The comparisons require conversions into equivalent units. 10 m is equal to 10^7 µm, so these quantities are equal. 10 kg is greater than 104 g as 10 kg equals 10,000 g, and 10^2 ms is greater than 10^5 ns since 10^2 ms equals 10^8 ns.

Step-by-step explanation:

To compare the quantities in each pair, we need to understand how to convert units so that we can compare like with like. This involves knowing the metric prefixes and their conversion factors.

1. A. 10 m vs. 107 µm:
   To compare meters (m) with micrometers (µm), note that 1 m = 106 µm. Therefore, 10 m = 10 * 106 µm = 107 µm. So, the two quantities are equal.

2. B. 10 cL vs. 10-24 C:
   For this comparison, it's assumed that 'C' refers to coulombs, however, this doesn't make sense because coulombs are a unit of electric charge, not volume or mass. Therefore, we cannot compare these two quantities as they are different properties.

3. C. 104 g vs. 10 kg:
   To compare grams (g) with kilograms (kg), note that 1 kg = 1000 g. Therefore, 10 kg = 10 * 1000 g = 10,000 g. So, 10 kg is greater than 104 g.

4. D. 105 ns vs. 102 ms:
   To compare nanoseconds (ns) with milliseconds (ms), note that 1 ms = 106 ns. Therefore, 102 ms = 100 * 106 ns = 108 ns. So, 102 ms is greater than 105 ns.