Rounding numbers

Rounding on a number line

Rounding asks a simple question: which round number is this closest to? To round 47 to the nearest 10, picture a number line from 40 to 50. 47 is 7 steps from 40 and 3 steps from 50, so it rounds to 50. The number line is the reason the rule works, and drawing one is the best way to check an answer.

The digit rule is a shortcut for the same picture. When you round to the nearest 10, the ones digit tells you how far past the lower ten you are. A ones digit from 1 to 4 means you are closer to the lower ten, and 6 to 9 means you are closer to the upper one.

What about exactly halfway? 45 is just as close to 40 as it is to 50. The convention taught in school is to round halves up, so 45 rounds to 50. That is why the rule says 5 or more rounds up.

Rounding to the nearest 10, 100 and 1000

• Nearest 10: 234 rounds to 230 and 235 rounds to 240. 970 is already a multiple of 10, so it stays 970.
• Nearest 100: 649 rounds to 600, because the tens digit is 4. 650 rounds to 700.
• Nearest 1000: 9327 rounds to 9000, because the hundreds digit is 3.
• Rounding up into a new place: 9960 to the nearest 100 is 10,000. The 99 hundreds become 100 hundreds, which is ten thousand.
• Larger numbers: 317,550 to the nearest 10,000 is 320,000, because the thousands digit is 7.

Rounding decimals

Decimals round in exactly the same way. To round to the nearest whole number, look at the tenths digit: 20.3 rounds to 20 and 7.5 rounds to 8. To round to one decimal place (the nearest tenth), look at the hundredths digit, so 4.68 rounds to 4.7. To round to two decimal places, look at the thousandths digit, so 3.14159 rounds to 3.14.

Watch for a zero that matters. 2.96 to one decimal place is 3.0, not 3: the question asked for one decimal place, and the 0 shows the answer is accurate to the nearest tenth. Rounding up can also ripple left, as in 97.993 to the nearest whole number, which is 98.

Money is rounding to two decimal places in disguise. A price worked out as $4.857 per item is $4.86 to the nearest cent.

Why we round

Rounding makes numbers easier to say, remember and work with. A crowd of 48,213 is about 48,000. Before adding 777 and 318, rounding each to the nearest hundred gives 800 + 300 = 1100, so an exact answer of 1095 looks right and 10,095 clearly doesn't.

In word problems, the situation decides the rounding. If a recipe needs 2.3 bags of flour, you buy 3 bags, even though 2.3 rounds to 2. That is rounding up for a practical reason, which is a different skill from rounding to the nearest.

How it is taught in school

In the US, Common Core introduces rounding whole numbers to the nearest 10 or 100 in grade 3 (3.NBT.A.1). Grade 4 extends this to rounding multi-digit whole numbers to any place (4.NBT.A.3), and grade 5 adds rounding decimals to any place (5.NBT.A.4).

In England, rounding starts in Year 4: any number to the nearest 10, 100 or 1000, and decimals with one decimal place to the nearest whole number. Year 5 covers numbers up to 1,000,000 to the nearest 10, 100, 1000, 10,000 and 100,000, and decimals with two decimal places to the nearest whole number and to one decimal place. In Year 6, pupils round any whole number to a required degree of accuracy and solve problems that need rounded answers.

How parents can help

• Draw a quick number line for any question your child finds tricky. Seeing where the number sits makes the rule make sense.
• Round prices in the store: is this closer to $3 or $4? Roughly how much will the whole basket cost?
• Talk about the halfway case. Ask what 65 rounds to and why, then try 650 to the nearest hundred and 6.5 to the nearest whole number.
• Turn it around with a puzzle: what is the smallest whole number that rounds to 400 when rounded to the nearest hundred? (350.) And the largest? (449.)
• Print a fresh worksheet, mark it with the answer key, and read the worked steps for any question that went wrong.