🔢 MathGrade 5Lesson 17
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Metric and Customary Conversions

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Learning Objectives

  • 1Identify common metric units of length, mass, and capacity
  • 2Identify common customary units of length, weight, and capacity
  • 3Convert between metric units by multiplying or dividing by powers of 10
  • 4Convert between customary units using the standard conversion factors
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Mini Lesson

Measurements come in two big systems. The metric system uses meters, grams, and liters and converts by powers of 10. The customary system uses inches, pounds, and gallons and uses memorized conversion factors. Knowing both systems lets you read recipes, weather reports, and science labels anywhere in the world.

The Metric System

  • Length: millimeter (mm), centimeter (cm), meter (m), kilometer (km).
  • Mass: milligram (mg), gram (g), kilogram (kg).
  • Capacity: milliliter (mL), liter (L).
  • Each unit is 10, 100, or 1,000 times bigger or smaller than the next: 1 km = 1,000 m, 1 m = 100 cm, 1 cm = 10 mm.
  • To go from a larger metric unit to a smaller one, multiply by 10, 100, or 1,000. To go from smaller to larger, divide.

The Customary System

  • Length: inch (in), foot (ft), yard (yd), mile (mi). 1 ft = 12 in, 1 yd = 3 ft, 1 mi = 5,280 ft.
  • Weight: ounce (oz), pound (lb), ton. 1 lb = 16 oz, 1 ton = 2,000 lb.
  • Capacity: cup (c), pint (pt), quart (qt), gallon (gal). 1 pt = 2 c, 1 qt = 2 pt, 1 gal = 4 qt.
  • Customary conversion factors are not powers of 10, so they must be memorized.

How to Convert

  • Larger unit to smaller unit: multiply. Example: 3 m = 3 x 100 = 300 cm.
  • Smaller unit to larger unit: divide. Example: 240 in = 240 / 12 = 20 ft.
  • Always write the unit next to the number — a number without units is not a measurement.
  • Estimate first to catch mistakes: 5 km should give a much bigger number of meters, not a smaller one.

When to Use Each System

  • Most countries and all science labs use the metric system.
  • The United States uses the customary system for everyday measurements like miles per hour and pounds of food.
  • Recipes and product labels often list both systems side by side.
Metric Length LadderMetric Length Ladderkmkilometermmetercmcentimetermmmillimeterx 1000x 100x 10÷ 1000÷ 100÷ 10Down the ladder: multiply. Up the ladder: divide.Each step is a power of 10.
Customary Conversion TableCustomary Conversion TableLength1 ft = 12 in1 yd = 3 ft1 mi = 5,280 ftin = inch, ft = foot, yd = yard, mi = mileWeight1 lb = 16 oz1 ton = 2,000 lboz = ounce, lb = poundCapacity1 pt = 2 c1 qt = 2 pt1 gal = 4 qtc = cup, pt = pint, qt = quart, gal = gallonMultiply to go from a larger unit to a smaller unit.
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Tip: when you forget a customary fact, picture the object. A foot is roughly the length of a standard ruler (12 in). A gallon of milk is 4 quarts. Pictures stick — numbers fade.

Vocabulary
metric
A measurement system based on powers of 10. Uses meters, grams, and liters.
customary
A measurement system used mainly in the United States. Uses inches, pounds, and gallons.
conversion
Changing a measurement from one unit to another while keeping the same amount.
unit
A standard amount used to measure something, like a meter, a pound, or a quart.
equivalent
Two measurements that name the same amount in different units, like 1 ft and 12 in.
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