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Estimation and rounding

Rounding is how a person makes a number easier to think about, and the point of it is the thinking rather than the rule. A child who rounds 4,732 to 4,700 and then to 5,000 without noticing which one the question wanted has learned the procedure and missed what it is for.

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Rounding to the nearest hundred

Round 4,732 to the nearest hundred.

  1. The hundreds digit is 7, so the answer is either 4,700 or 4,800.
  2. Look at the digit to its right — the tens digit, 3.
  3. 3 is less than 5, so 4,732 is closer to 4,700.
  4. The answer is 4,700.

Worth knowing. Only the digit immediately to the right decides it. 4,749 rounds to 4,700 even though the 49 looks close to 50, because the tens digit is 4.

Landing exactly on the halfway point

Round 250 to the nearest hundred.

  1. The hundreds digit is 2, so the answer is either 200 or 300.
  2. The tens digit is 5, which is exactly halfway.
  3. The agreed rule is that a half rounds up.
  4. The answer is 300.

Worth knowing. This one is a convention, not a fact — 250 really is the same distance from both. It is worth saying so, because a child who is told it is "closer to 300" will not believe it, and will be right.

Where it usually goes wrong

  • Rounding twice: 4,749 to 4,750 to 4,800, when the question asked for the nearest hundred.
  • Looking at the whole rest of the number instead of the single digit to the right.
  • Forgetting the places to the right become zeros, so 4,732 to the nearest hundred comes out as 47.

The Professor rounds before he calculates, so he knows roughly what the answer should be. When the exact answer is nowhere near it, he has found a mistake.

Practise it

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Questions teachers and parents ask

When is rounding taught?

Rounding to the nearest 10 and 100 is grade 3 (3.NBT.A.1), and rounding multi-digit numbers to any place is grade 4 (4.NBT.A.3). Estimating to check an answer runs alongside it from grade 3 onward.

Why does a half round up?

Because someone had to decide, and up is the convention most school curricula use. 250 is genuinely the same distance from 200 and 300, so no rule can be derived from the numbers — it is an agreement so that everyone gets the same answer.

Is estimating the same as rounding?

Rounding is one way of estimating. Estimating is the wider habit: working out roughly what an answer should be before finding it exactly, so a wrong answer stands out. A child who estimates 4,732 + 2,891 as about 7,600 will notice if their column work says 760.

Which digit decides it?

Only the one immediately to the right of the place being rounded to. 4,749 to the nearest hundred is 4,700, because the tens digit is 4 — the 9 after it does not get a vote.

Where this shows up

Standards

  • 3.NBT · Number and operations in base ten
  • 4.NBT · Number and operations in base ten
  • 5.NBT · Number and operations in base ten

Formats