What is the method for converting between metric prefixes?

What is the method for converting between metric prefixes?

• A. Multiply the numbers and move the decimal
• B. Add the exponents and move the decimal
• C. Look at the exponents and move the decimal point accordingly.
• D. Look at the decimal point and adjust the prefix by trial

Answer: (C)

Converting between metric prefixes hinges on powers of ten. Each prefix maps to an exponent of 10, so changing from one prefix to another means shifting the decimal point by the difference in those exponents. For example, converting 2.4 kilometers to meters uses exponents 3 (kilo) and 0 (base), a difference of 3, so you move the decimal three places to the right to get 2400 m. Conversely, converting 1500 microseconds to milliseconds uses exponents −6 and −3; the difference is 3, so you move the decimal three places to the left to obtain 1.5 ms. This method consistently encodes how many factors of 10 separate the prefixes. Other approaches that multiply, add exponents, or guess with trial don’t reflect the fixed 10^n relationship between prefixes.

Converting between metric prefixes hinges on powers of ten. Each prefix maps to an exponent of 10, so changing from one prefix to another means shifting the decimal point by the difference in those exponents. For example, converting 2.4 kilometers to meters uses exponents 3 (kilo) and 0 (base), a difference of 3, so you move the decimal three places to the right to get 2400 m. Conversely, converting 1500 microseconds to milliseconds uses exponents −6 and −3; the difference is 3, so you move the decimal three places to the left to obtain 1.5 ms. This method consistently encodes how many factors of 10 separate the prefixes. Other approaches that multiply, add exponents, or guess with trial don’t reflect the fixed 10^n relationship between prefixes.