Measurement & Unit Conversion

5.H.1Customary units01/04

Convert customary units (length, weight, volume).

Step01of 04

Customary units are the U.S. system. Conversions aren't powers of 10 — you have to memorize them.

Length	→1 ft = 12 in; 1 yd = 3 ft; 1 mi = 5,280 ft
Weight	→1 lb = 16 oz; 1 ton = 2,000 lb
Volume	→1 cup = 8 fl oz; 1 pt = 2 cups; 1 qt = 2 pt; 1 gal = 4 qt
Time	→1 min = 60 sec; 1 hr = 60 min

5.H.1 — Convert customary units (length, weight, volume).

Step 01 of 04

Customary units are the U.S. system. Conversions aren't powers of 10 — you have to memorize them.

Length	→1 ft = 12 in; 1 yd = 3 ft; 1 mi = 5,280 ft
Weight	→1 lb = 16 oz; 1 ton = 2,000 lb
Volume	→1 cup = 8 fl oz; 1 pt = 2 cups; 1 qt = 2 pt; 1 gal = 4 qt
Time	→1 min = 60 sec; 1 hr = 60 min

Step 02 of 04

Bigger to smaller: MULTIPLY. Smaller to bigger: DIVIDE.

Step 03 of 04

Examples:

5 ft to inches	→5 × 12 = 60 in
3 lb to ounces	→3 × 16 = 48 oz
2 gal to cups	→2 × 4 × 2 × 2 = 32 cups (gal → qt → pt → cups)
48 in to ft	→48 ÷ 12 = 4 ft
64 oz to lb	→64 ÷ 16 = 4 lb

Step 04 of 04

Multi-step conversions. Chain them: gallons → quarts → pints → cups → fluid ounces.

1 gal = 4 qt = 8 pt = 16 cups = 128 fl oz

Key insight

Memorize the conversions in each system. Bigger → smaller: multiply. Smaller → bigger: divide. Multi-step conversions chain through intermediate units.

5.H.2 — Convert metric units.

Step 01 of 04

Metric is much easier — every conversion is a power of 10.

Length	→1 km = 1,000 m; 1 m = 100 cm = 1,000 mm
Mass	→1 kg = 1,000 g; 1 g = 1,000 mg
Volume	→1 L = 1,000 mL

Step 02 of 04

Common prefixes:

kilo-	→1,000
centi-	→1/100
milli-	→1/1,000

So a kilometer is 1,000 meters; a centimeter is 1/100 of a meter; a milligram is 1/1000 of a gram.

Step 03 of 04

Convert by shifting the decimal.

4.5 km to m	→4,500 m (× 1,000)
320 cm to m	→3.20 m (÷ 100)
2.5 L to mL	→2,500 mL
750 mg to g	→0.75 g

Step 04 of 04

Comparing measurements in different units. Convert to the same unit first.

Is 1.2 km longer than 1,500 m? Convert 1.2 km = 1,200 m. So 1,500 m is longer.

Key insight

Metric is all powers of 10 — just shift the decimal. Memorize the prefix meanings (kilo, centi, milli). Always convert to the same unit before comparing.

5.H.3 — Multi-step measurement word problems.

Step 01 of 04

Multi-step measurement problems combine conversion with addition, subtraction, multiplication, or division.

Step 02 of 04

Worked example. A bottle holds 2 L. You drink 350 mL. How much remains?

Convert: 2 L = 2,000 mL.

2, 000 - 350 = 1, 650 mL = 1.65 L

Step 03 of 04

Recipe scaling. Recipe needs 1/4 cup of butter per batch. You're making 6 batches. How many TABLESPOONS of butter? (1 cup = 16 Tbsp)

6 \times \frac{1}{4} = \frac{6}{4} = 1 \frac{1}{2} cups

1 \frac{1}{2} \times 16 = 24 Tbsp

Step 04 of 04

Time problem. You spend 1 hr 25 min on homework Monday and 50 min Tuesday. Total time?

1 hr 25 min = 85 min

85 + 50 = 135 min = 2 hr 15 min

Key insight

Convert to a common unit before adding or subtracting. Many real-world problems chain conversion with arithmetic. Always answer with units (and convert to the unit the question wants).

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