Metric Units of Measurement
Semester 4B · Chapter 10 · Lesson 1 · MATH-4B-C10-L01
Before you begin: prerequisite check
Recall: 3B metric conversions; place-value regrouping. Attempt these questions independently first.
How many centimeters make one meter?
Show answer and reasoning
1 meter equals 100 centimeters.
How many minutes make one hour?
Show answer and reasoning
A full hour contains 60 minutes.
Find 3/4 of 20.
Show answer and reasoning
20 ÷ 4 = 5; take three groups of five.
Key vocabulary
- metric unit
- meter, gram or liter family with decimal relationships
- customary unit
- inch, foot, pound or gallon family with its own conversion factor
- mixed units
- one measurement written using two units
- reference whole
- the full quantity of which a fraction is taken
Understand the concept
A measurement is a number together with a unit. The number alone is not enough: 3 kilometers and 3 meters are different lengths. In the metric system, move between units using groups of ten, one hundred, or one thousand. For example, 2 kilometers 35 meters means 2,035 meters because each kilometer contributes 1,000 meters. When subtracting mixed measures, first rewrite both in the same small unit, or exchange one large unit for its equivalent small units. Always check that the answer's unit matches the question.
Fully worked examples and immediate checks
Read each example, predict how to begin, then follow its numerical explanation. The check below it is a fresh problem.
Worked example 1
Convert 5 km 738 m entirely to m.
Each km is 1,000 m. Multiply 5×1,000, then add 738: 5,738 m.
Check 1: try it yourself
Convert 3 m 21 cm entirely to cm.
Show answer and reasoning
Each m is 100 cm. Multiply 3×100, then add 21: 321 cm.
Worked example 2
Rename 687 cm as whole m and leftover cm.
Dividing by 100 gives 6 whole m with 87 cm remaining.
Check 2: try it yourself
Rename 5,613 m as whole km and leftover m.
Show answer and reasoning
Dividing by 1000 gives 5 whole km with 613 m remaining.
Worked example 3
A measured quantity is 4 m 17 cm. Another quantity of 2 m 34 cm is taken away. How much remains in cm?
Convert both measurements to cm, then subtract: 417−234=183.
Check 3: try it yourself
A measured quantity is 10 m 27 cm. Another quantity of 8 m 54 cm is taken away. How much remains in cm?
Show answer and reasoning
Convert both measurements to cm, then subtract: 1,027−854=173.
Guided practice
Convert 5 kg 903 g entirely to g.
Show answer and reasoning
Each kg is 1,000 g. Multiply 5×1,000, then add 903: 5,903 g.
Rename 5,901 mL as whole L and leftover mL.
Show answer and reasoning
Dividing by 1000 gives 5 whole L with 901 mL remaining.
A measured quantity is 4 L 462 mL. Another quantity of 2 L 924 mL is taken away. How much remains in mL?
Show answer and reasoning
Convert both measurements to mL, then subtract: 4,462−2,924=1,538.
Which is greater: 9 m or 899 cm? State the difference in cm.
Show answer and reasoning
9 m=900 cm, exactly one more than 899.
A quantity measures 4 km 782 m. Explain why writing it as 4,782 m does not change its size.
Show answer and reasoning
4 of the larger unit equals 4,000 of the smaller unit. Adding 782 preserves the same length.
Independent practice
Convert 3 m 52 cm entirely to cm.
Show answer and reasoning
Each m is 100 cm. Multiply 3×100, then add 52: 352 cm.
Rename 499 cm as whole m and leftover cm.
Show answer and reasoning
Dividing by 100 gives 4 whole m with 99 cm remaining.
A measured quantity is 8 kg 174 g. Another quantity of 6 kg 348 g is taken away. How much remains in g?
Show answer and reasoning
Convert both measurements to g, then subtract: 8,174−6,348=1,826.
Which is greater: 7 m or 699 cm? State the difference in cm.
Show answer and reasoning
7 m=700 cm, exactly one more than 699.
A quantity measures 9 m 49 cm. Explain why writing it as 949 cm does not change its size.
Show answer and reasoning
9 of the larger unit equals 900 of the smaller unit. Adding 49 preserves the same length.
Convert 4 kg 939 g entirely to g.
Show answer and reasoning
Each kg is 1,000 g. Multiply 4×1,000, then add 939: 4,939 g.
Rename 4,601 g as whole kg and leftover g.
Show answer and reasoning
Dividing by 1000 gives 4 whole kg with 601 g remaining.
A measured quantity is 10 L 160 mL. Another quantity of 8 L 321 mL is taken away. How much remains in mL?
Show answer and reasoning
Convert both measurements to mL, then subtract: 10,160−8,321=1,839.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Convert 4 L 40 mL entirely to mL. Explain or sketch the mathematical relationship.
Show answer and reasoning
Each L is 1,000 mL. Multiply 4×1,000, then add 40: 4,040 mL. State which quantities or geometric properties justify the method.
A learner claims: “1 kilometer equals 100 meters.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: 1 kilometer equals 1,000 meters. For example, 2 km = 2,000 m. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Convert 8 kg 801 g entirely to g.
Show answer and reasoning
Each kg is 1,000 g. Multiply 8×1,000, then add 801: 8,801 g.
Rename 8,675 mL as whole L and leftover mL.
Show answer and reasoning
Dividing by 1000 gives 8 whole L with 675 mL remaining.
A measured quantity is 5 L 345 mL. Another quantity of 3 L 691 mL is taken away. How much remains in mL?
Show answer and reasoning
Convert both measurements to mL, then subtract: 5,345−3,691=1,654.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.