What is the trick for converting metric units?

What is the trick for converting metric units?

• A. Subtract the exponent for the first prefix from the second prefix and move the decimal accordingly.
• B. Divide by 10.
• C. Multiply the exponents.
• D. Add the exponents.

Answer: (A)

Metric prefixes are powers of ten, so changing units is just moving the decimal point. To switch from one prefix to another, subtract the exponent of the current prefix from the exponent of the target prefix. that difference tells you how far to shift the decimal, and the direction follows the sign: a negative result means move the decimal to the right, a positive result means move it to the left. For example, converting 3.6 kilometers to meters: kilometers have exponent 3 and meters have exponent 0. Difference is 0 − 3 = −3, so move the decimal three places to the right: 3.6 km = 3600 m. Another example: converting 12 centimeters to meters: centimeter exponent is −2, meter is 0. Difference is 0 − (−2) = +2, so move the decimal two places to the left: 12 cm = 0.12 m. This approach captures why the decimal shift works and why the difference in exponents governs the conversion.

Metric prefixes are powers of ten, so changing units is just moving the decimal point. To switch from one prefix to another, subtract the exponent of the current prefix from the exponent of the target prefix. that difference tells you how far to shift the decimal, and the direction follows the sign: a negative result means move the decimal to the right, a positive result means move it to the left.

For example, converting 3.6 kilometers to meters: kilometers have exponent 3 and meters have exponent 0. Difference is 0 − 3 = −3, so move the decimal three places to the right: 3.6 km = 3600 m.

Another example: converting 12 centimeters to meters: centimeter exponent is −2, meter is 0. Difference is 0 − (−2) = +2, so move the decimal two places to the left: 12 cm = 0.12 m.

This approach captures why the decimal shift works and why the difference in exponents governs the conversion.