Questions: Converting Metric Units

Question 1

Convert 4.7 kilometers to meters.

• A. 0.0047 m
• B. 47 m
• C. 470 m
• D. 4,700 m

Answer: (D)

1 kilometer = 1,000 meters, so multiply by 1,000. Multiplying by 1,000 moves the decimal point 3 places to the right: 4.7 → 4,700. The answer passes the intuition check: meters are smaller than kilometers, so going from km to m should give a larger number. Options A and B result from moving the decimal the wrong way or the wrong number of places.

Question 2

A student converts 850 centimeters to meters and gets 85,000. They moved the decimal 3 places to the right. What went wrong?

• A. They should have moved the decimal only 2 places, not 3
• B. Converting to a larger unit means dividing — moving the decimal LEFT — not right; the correct answer is 8.5 m
• C. There are only 10 centimeters in a meter, not 100
• D. The answer is correct

Answer: (B)

The critical rule: going to a larger unit means you need fewer of them, so the number gets smaller — move the decimal LEFT (divide). 1 meter = 100 centimeters, so 850 cm ÷ 100 = 8.5 m. Moving right (multiplying) is used when converting to a smaller unit. The student applied the right number of places (2 for cm→m, not 3) but also moved in the wrong direction — a compound error.

Question 3

Converting a measurement from a smaller unit to a larger unit generally produces a larger number (for example, 500 cm becomes a number larger than 500 when converted to meters).

• T. True
• F. False

Answer: False

The opposite is true. Converting to a larger unit always produces a smaller number — you need fewer large units to describe the same length. 500 cm = 5 m, and 5 is much smaller than 500. The intuition check 'larger unit → smaller number, smaller unit → larger number' is the built-in sanity check for every metric conversion.

Question 4

Multiplying a number by 1,000 and moving its decimal point 3 places to the right describe the exact same mathematical operation.

• T. True
• F. False

Answer: True

Moving the decimal point one place to the right multiplies by 10 (5.0 → 50.0). Moving it 2 places multiplies by 100; 3 places multiplies by 1,000. The decimal-point shift notation is just a shorthand for the underlying place-value arithmetic. This connection is why metric conversions are so straightforward: each prefix step corresponds to exactly one decimal place shift.

Question 5

How can you quickly check whether you moved the decimal point in the right direction when converting between metric units?

Model answer: Ask: am I converting to a larger unit or a smaller unit? If larger (e.g., cm → m, g → kg), the number should get smaller — move the decimal left. If smaller (e.g., m → cm, kg → g), the number should get larger — move the decimal right. If your answer violates this — for instance, if you converted to meters and got a bigger number than your centimeter value — you moved the decimal the wrong way.

This direction check is more reliable than trying to remember 'multiply or divide' for each pair of units. It is grounded in a simple physical truth: larger units need fewer of them to cover the same quantity. Any answer that puts more of a larger unit than a smaller unit for the same measurement is automatically wrong.