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Measurement and units

Measuring only works if everyone agrees what the unit is, and two systems are in daily use — metric and customary — so most measurement work is converting between sizes of the same thing. Going from a big unit to a small one multiplies, because it takes many small ones to make one big one, and going the other way divides.

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Going down: metres to centimetres

How many centimetres are in 4 metres?

  1. One metre is 100 centimetres.
  2. Centimetres are smaller, so it takes more of them — the answer will be bigger than 4.
  3. Multiply: 4 x 100.
  4. The answer is 400 centimetres.

Worth knowing. Multiplying by 100 moves every digit two places and leaves the digits alone. That is why metric conversions are quicker than customary ones: 12 and 5,280 have to be multiplied out properly.

Going up: inches to feet

How many feet are in 60 inches?

  1. One foot is 12 inches.
  2. Feet are bigger, so it takes fewer of them — the answer will be smaller than 60.
  3. Divide: 60 divided by 12.
  4. The answer is 5 feet.

Worth knowing. Not every number of inches is a whole number of feet — 50 inches is 4 feet with 2 inches left over. Every question here is chosen so that it comes out whole.

Where it usually goes wrong

  • Multiplying when the answer should get smaller, so 60 inches becomes 720 feet.
  • Swapping the factors — 3 feet in a yard and 12 inches in a foot get used the wrong way round, and 5 yards becomes 60 feet.
  • Trying to cross between systems. Inches and centimetres have no whole-number relationship, and nothing here asks you to convert from one system to the other.

The Professor asks one question before he does anything: will the answer be a bigger number or a smaller one? A metre is more than a centimetre, so metres into centimetres has to give a bigger number. That single check catches most wrong conversions.

Practise it

All level paths

Questions teachers and parents ask

How do I know whether to multiply or divide?

Ask whether the unit you are moving to is bigger or smaller than the one you started with. A smaller unit means you need more of them, so multiply; a bigger unit means fewer, so divide. Checking the size of your answer against that catches almost every mistake in the topic.

Why are metric conversions easier than customary ones?

Because every step is a power of ten, so converting moves the digits and does not change them. Customary units step by 12, 3, 16 and 5,280, and each of those is a multiplication you have to work out.

Do I need to know how many centimetres are in an inch?

Not here. One inch is 2.54 centimetres, which is not a whole number, so a sheet built on it would have answers like 10.16 on it. Every conversion on this site stays inside one system, which is what grade 4 asks for.

When is unit conversion taught?

Knowing the relative sizes of units within one system, and expressing a larger unit in terms of a smaller one, is grade 4 (4.MD.A.1). Converting in both directions and using it in multi-step problems is grade 5 (5.MD.A.1).

Where this shows up

Standards

  • 4.MD · Measurement and data
  • 5.MD · Measurement and data
  • CCSS.MATH.CONTENT.4.MD.A.1 — Know the relative sizes of measurement units within one system, and express a larger unit in terms of a smaller one.
  • CCSS.MATH.CONTENT.5.MD.A.1 — Convert among different-sized standard measurement units within a given system, and use these conversions in multi-step problems.

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