Question

What metric prefixes correspond to the following powers of \(10 ?\) a) \(10^{3}\) b) \(10^{-2}\) c) \(10^{-3}\)

Short answer

Question: Determine the metric prefixes for the following powers of 10: a) \(10^3\), b) \(10^{-2}\), c) \(10^{-3}\). Answer: a) \(10^3\) = Kilo (k), b) \(10^{-2}\) = Centi (c), c) \(10^{-3}\) = Milli (m).

Step-by-step solution

Identify the powers of 10 with their metric prefixes

To solve this exercise, we need to identify the correct metric prefixes for the given powers of 10. Here is a helpful reference table of metric prefixes: 1. Kilo (k) = \(10^3\) 2. Hecto (h) = \(10^2\) 3. Deca (da) = \(10^1\) 4. Base unit (no prefix) = \(10^0\) 5. Deci (d) = \(10^{-1}\) 6. Centi (c) = \(10^{-2}\) 7. Milli (m) = \(10^{-3}\) 8. Micro (µ) = \(10^{-6}\) 9. Nano (n) = \(10^{-9}\) 10. Pico (p) = \(10^{-12}\) Now, let's find the metric prefixes for each power of 10.

Match each power of 10 with the corresponding metric prefix

a) \(10^3\) From our reference table, we can see that \(10^3\) corresponds to the metric prefix Kilo (k). b) \(10^{-2}\) From our reference table, we can see that \(10^{-2}\) corresponds to the metric prefix Centi (c). c) \(10^{-3}\) From our reference table, we can see that \(10^{-3}\) corresponds to the metric prefix Milli (m).

Summary

The metric prefixes corresponding to the given powers of 10 are: a) \(10^3\) = Kilo (k) b) \(10^{-2}\) = Centi (c) c) \(10^{-3}\) = Milli (m)