3 mistakes learners make with rounding and significant figures, each one named and explained.
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.
48 627 to the nearest thousand is answered as 48 000.
Chopping looks like rounding down and it is right about half the time, so it survives a long while before anybody notices.
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.
Rounding asks which one it is nearer to. Chopping never asks.
1 250 000 to 2 significant figures is answered as 1 200 000.
Exactly half is genuinely awkward, and rounding down feels like the safer, smaller choice.
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.
Five and above rounds up. It is a convention, not a judgement, which is why it is worth simply knowing.
Asked for the nearest thousand you give 48 600, or asked for 2 significant figures you give 1 250 000.
The instruction and the counting happen in different parts of your head, and one of them wins.
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.
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.