The Metric System: Homework

Each step on the metric ladder is a power of ten. Going to a smaller unit multiplies, and going to a bigger one divides.

Part A — Convert / 10

Write the answer with its unit.

Each of these has a trap. Ask whether the unit you are going to is bigger or smaller.

1.
Is 3 L the same as 30 mL or 3,000 mL?Answer
2.
Which is longer, 0.5 m or 45 cm? Change both to centimeters.Answer
3.
A student divides 4 km by 1,000 and says 4 km is 0.004 m. What should it be?Answer
4.
Which is greater, 2,500 mg or 2 g? (1 g = 1,000 mg)Answer
5.
How many centimeters are in one kilometer? (Kilo means a thousand, and a meter has 100 centimeters.)Answer

Real numbers. The golf ball and soccer ball come from the official rules. Change each unit the way the question asks.

1.
Official sizes:
Ball Size Mass
Golf ball diameter at least 42.67 mm at most 45.93 g
Soccer ball, size 5 circumference 68 to 70 cm 410 to 450 g
a. Give the golf ball's smallest legal diameter in centimeters.Answer
b. Give the golf ball's smallest legal diameter in meters.Answer
c. Give the soccer ball's greatest mass in kilograms.Answer
d. How many grams heavier is the soccer ball's greatest mass than the golf ball's greatest mass?Answer
2.
Three real lengths: a marathon is 42.195 km, an Olympic pool is 50 m long, and a golf ball is 42.67 mm across.
a. Give the marathon in meters.Answer
b. Put the three lengths in order from shortest to longest.Answer
c. How many Olympic pools laid end to end are as long as a marathon?Answer

Ball	Size	Mass
Golf ball	diameter at least 42.67 mm	at most 45.93 g
Soccer ball, size 5	circumference 68 to 70 cm	410 to 450 g

Think it through, then write your answer and one sentence about how you knew.

1.
Put these lengths in order from least to greatest: 0.8 km, 76,000 cm, 815 m and 79,500 mm. Change them all to meters first.Answer
2.
A bottle holds 1.5 L. How many 250 mL cups can you fill from it? Work in the same unit.Answer

Write your own, then work it.

1.
Write a problem about something you could measure that needs TWO different metric units, and solve it. Say which way you converted.Answer

Total / 25

Graded by

Notes

Part A — the conversions.

Part B — the answer.

Part C — the answers.

a. 4.267 cm b. 0.04267 m c. 0.45 kg d. 404.07 grams
a. 42,195 m b. 42.67 mm, then 50 m, then 42.195 km. In meters: 0.04267 < 50 < 42,195. c. 843.9 pools, so about 844

Part D — one correct answer, and what a good explanation says.

79,500 mm (79.5 m) < 76,000 cm (760 m) < 0.8 km (800 m) < 815 m. Converting to one unit makes them comparable.
6 cups. 1.5 L = 1,500 mL, and 1,500 ÷ 250 = 6.

Part E — what a good problem looks like.

Answers vary. A good one picks a unit for the job and converts one measurement to match, such as a 1.2 m ribbon cut into 15 cm pieces: 1.2 m = 120 cm, and 120 ÷ 15 = 8 pieces.