Rounding to the nearest 10 and 100

What it is

Rounding replaces a number with the nearest multiple of 10, 100 or 1,000, so it is easier to hold in your head and still close enough to be useful. To round to the nearest 10, find the two multiples of 10 the number sits between and take the nearer one: 168 sits between 160 and 170, and it is 8 past 160, so it rounds to 170. Rounding the same number to the nearest 100 uses a different pair of neighbours: 168 sits between 100 and 200, and it is 68 past 100, so it rounds to 200.

One digit decides which way it goes. Rounding to the nearest 10 is decided by the ones digit, and rounding to the nearest 100 by the tens digit: 4 or less and the number goes down to the multiple below, 5 or more and it goes up to the multiple above. A number exactly halfway goes up, which is the convention taught in English schools, so 145 rounds to 150 and 250 rounds to 300.

Rounding is used more often to check an answer than to produce one. Before working out 168 + 214 in column addition, a child who rounds to 170 and 210 knows the answer should be somewhere near 380, so a slipped column that gives an answer in the thousands gets noticed. Year 4 also asks pupils to estimate and check answers to a calculation, and rounding is how the estimate is made.

When children learn it

Rounding is a Year 4 requirement. The programme of study asks pupils to round any number to the nearest 10, 100 or 1,000. The Year 3 programme has no rounding requirement in it at all, so a child meeting rounding for the first time in Year 4 is meeting it on time. Year 5 extends it to numbers up to 1,000,000 and to the nearest 10,000 and 100,000, and Year 6 asks for any whole number rounded to a required degree of accuracy.

A Year 3 class that meets rounding early and a Year 4 class that meets it in the summer term are both doing what is asked of them.

What it looks like when it goes wrong

These patterns come up again and again in children's answers on this skill. Each one points at a specific missing idea, not carelessness.

• The number chopped rather than rounded. 168 to the nearest 10 answered as 160, or to the nearest 100 answered as 100. The digits after the column are being dropped rather than read, so every number goes down and a number never rounds up. The halfway case looks the same from the outside: 145 to the nearest 10 given as 140, where the rule taught is that halfway goes up.
• The number sent the wrong way. 143 to the nearest 10 answered as 150. This is the opposite habit, and it is usually rounding up by default rather than reading the deciding digit. Asking which two multiples of 10 the number sits between, and which of the two it is nearer, tends to correct it on the spot.
• The right rule used on the wrong column. Asked for 168 to the nearest 100, they answer 170. The rounding is done correctly, but to the nearest 10. Children who round reliably still lose track of which column was asked for, particularly on a page of questions that switches between 10 and 100.
• The deciding digit read in the wrong column. Asked what the 6 in 168 is worth, they answer 600, reading the digit one column further left than it stands. That is a place value gap rather than a rounding one. Rounding to the nearest 100 asks the child to look at the tens digit, and a child who cannot say which column a digit is standing in has no way to find it, so the rule they have been taught gets applied to whichever digit they pick.

How to help at home

• Draw the two neighbours. Write the multiple below and the multiple above at either end of a line, mark the number between them, and ask which end it is nearer. Numbersaurus shows the same line if a child pauses over a rounding question or answers it wrongly.
• Ask "the nearest what?" before anything else. Naming the column first is what stops a correct rounding rule landing on the wrong column.
• Agree the halfway rule once and keep to it: 5 or more goes up, and exactly halfway goes up.
• Use rounding for checking. Before a written calculation, ask roughly what the answer should be, then compare the worked answer with that estimate.

Other guides

• Place valueWhat each digit in a number is worth, what partitioning is, and the wrong answers that show the idea is missing.
• Four-digit numbersWhat the thousands column adds, why numbers with a zero inside them are the hard ones, and how Year 4 counts in 1,000s and compares beyond 1,000.
• Column additionThe written method from Year 3: carrying, lining up digits, and the errors to watch for.