Maths

Common mistakes in rounding and significant figures

3 mistakes learners make with rounding and significant figures, each one named and explained.

All common mistakes

Rounding replaces a number with the nearest tidy one, so the digit after the place you are rounding to is the only one that decides.

Cutting the digits off instead of rounding

What it looks like

48 627 to the nearest thousand is answered as 48 000.

Why it happens

Chopping looks like rounding down and it is right about half the time, so it survives a long while before anybody notices.

A worked example

Question. 48 627 to the nearest thousand

A common answer. 48 000, with the rest thrown away

The answer. 49 000

Why. 627 is more than half of a thousand, so the number is nearer to 49 000 than to 48 000.

Put the two side by side

48 627 is 627 past 48 000.
48 627 is 373 short of 49 000.

Rounding asks which one it is nearer to. Chopping never asks.

Rounding a 5 down

What it looks like

1 250 000 to 2 significant figures is answered as 1 200 000.

Why it happens

Exactly half is genuinely awkward, and rounding down feels like the safer, smaller choice.

A worked example

Question. 1 250 000 to 2 significant figures

A common answer. 1 200 000

The answer. 1 300 000

Why. The agreed rule is that a 5 rounds up, so that everybody gets the same answer.

Put the two side by side

1 249 999 rounds down to 1 200 000.
1 250 000 rounds up to 1 300 000.

Five and above rounds up. It is a convention, not a judgement, which is why it is worth simply knowing.

Rounding to the wrong column

What it looks like

Asked for the nearest thousand you give 48 600, or asked for 2 significant figures you give 1 250 000.

Why it happens

The instruction and the counting happen in different parts of your head, and one of them wins.

A worked example

Question. 48 627 to the nearest thousand

A common answer. 48 600, which is the nearest hundred

The answer. 49 000

Why. The thousands digit is the one being decided, so the hundreds digit is what does the deciding.

Put the two side by side

Nearest hundred: 48 600.
Nearest thousand: 49 000.

Underline the column you are rounding to before you look at anything else.

WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.

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