Lesson 5 of 8 · Grades 3 to 5
Converting units
A measurement can be written in more than one unit. Converting means changing the unit without changing the amount. The whole skill is choosing between multiplying and dividing, and knowing the fact for the units in front of you.
Same amount, new unit
Converting a measurement means writing the same amount with a different unit. A board that is 2 m long is also 200 cm long. Nothing about the board changes; only the unit and the number do. The golden rule is that the amount must stay the same, so a sentence such as "2 m = 2 cm" is never true.
Two questions decide every conversion. Are you going to a smaller unit or a larger one? And what is the fact that joins the two units? Once you know those two things, the arithmetic is a single multiplication or division.
Going smaller: multiply
When you change to a smaller unit, the number of units grows. A metre holds 100 centimetres, so 3 m is 3 × 100 = 300 cm. A kilogram holds 1,000 grams, so 3 kg is 3 × 1,000 = 3,000 g. A minute holds 60 seconds, so 3 minutes is 3 × 60 = 180 seconds. Remember the direction with a simple sentence: going smaller, multiply.
Going larger: divide
When you change to a larger unit, the number of units shrinks. It takes 100 centimetres to make one metre, so 500 cm is 500 ÷ 100 = 5 m. It takes 1,000 grams to make one kilogram, so 8,000 g is 8 kg. The same rule works for millilitres and litres: 2,500 mL is 2,500 ÷ 1,000 = 2.5 L. Going larger, divide.
The metric facts all use powers of ten: 10, 100 and 1,000. That is why metric conversions can be done by moving the decimal point. Multiplying by 100 moves it two places to the right, and dividing by 1,000 moves it three places to the left. 4 m becomes 400 cm, and 2,500 mL becomes 2.5 L.
Customary facts are different
Customary units do not share one pattern, so each conversion needs its own fact. Change feet to inches with 12: 6 ft is 6 × 12 = 72 in. Change yards to feet with 3, pounds to ounces with 16, and quarts to cups with 4. When a fact is not a multiple of ten, the shortcut with the decimal point does not work, so multiply or divide on paper.
Two steps at once
Sometimes the unit you have and the unit you want are two steps apart. Changing kilometres to centimetres means going through metres: 2 km is 2,000 m, and 2,000 m is 200,000 cm. You can also multiply by both facts at once: 2 × 1,000 × 100 = 200,000. Break the problem into single steps when the numbers feel big, and write the unit down at every step so the answer keeps its meaning.
Always check a conversion with an estimate. When you change to a smaller unit, the number must be larger than the one you started with. If 5 m becomes 0.05 cm, something went the wrong way, because centimetres are smaller than metres and there must be more of them.
Watch out for this
The most common mistake is choosing the wrong operation. Ask which unit is smaller before you compute. Metres are smaller than kilometres, so 3,000 m is 3 km, not 3,000 km. Pounds are smaller than tons, so a car does not weigh 2 tons of pounds; mixing the unit with the wrong word also hides the error. Say the unit inside the sentence and check it sounds right.
Worked example
A ribbon is 2 m 40 cm long. Write the length in millimetres.
Step 1: decide on the direction. Millimetres are smaller than metres and centimetres, so the number will grow.
Step 2: change the metres to millimetres. 1 m = 1,000 mm, so 2 m = 2,000 mm.
Step 3: change the centimetres to millimetres. 1 cm = 10 mm, so 40 cm = 400 mm.
Step 4: add the parts. 2,000 mm + 400 mm = 2,400 mm. Check with an estimate: a ribbon a little over two metres is about 2,400 mm.
Answer: 2,400 mm.
Remember
- Going to a smaller unit, multiply; going to a larger unit, divide.
- The metric facts are 10, 100 and 1,000.
- The customary facts include 12 inches, 3 feet, 16 ounces and 4 cups.
- A two-step conversion can be done as two single steps.
Try it
Answer the five questions below. Work them out first, then open each answer to check.
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Convert 4 metres to centimetres.
Show answer
400 cm. Metres are larger than centimetres, so multiply: 4 × 100 = 400 cm.
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Convert 300 centimetres to metres.
Show answer
3 m. Centimetres are smaller than metres, so divide: 300 ÷ 100 = 3 m.
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Convert 7 kilograms to grams.
Show answer
7,000 g. Multiply by 1,000: 7 × 1,000 = 7,000 g.
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Convert 2,500 millilitres to litres.
Show answer
2.5 L. Divide by 1,000: 2,500 ÷ 1,000 = 2.5 L.
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Convert 6 feet to inches.
Show answer
72 in. Multiply by 12: 6 × 12 = 72 in.
Puzzle · Missing digit
Puzzle time
1.2 litres is the same as 1,?00 millilitres. Which digit belongs in the box?
Show a hint
Multiply 1.2 by 1,000 to change litres into millilitres.
Show the answer
Answer: 2. 1.2 × 1,000 = 1,200, so the missing hundreds digit is 2.