Rounding

News reports say a city has "about 14 million people", not 13.953 million. Nothing is being hidden — those fine digits simply do not matter. Rounding swaps a number for a nearby, easier number that is close enough.

Why round at all

• Reporting: populations, box office, distances — extra digits carry no information;
• Estimating: total up a shopping cart in whole tens first; estimation starts with rounding;
• Readability: $0.33333\ldots$ comfortably becomes $0.33$.

One principle rules them all: pick the nearest neighbour.

Which neighbour is nearest: check the next digit

To round 47 to the nearest ten, notice 47 sits between 40 and 50 — it is 3 away from 50 and 7 away from 40, so 50 wins. Round 438 to the nearest hundred: between 400 and 500, it is 38 from 400 and 62 from 500, so 400 wins.

No need to measure every time — look at the digit just right of the place you keep: below 5, round down; 5 or above, round up. A number sitting exactly on the midpoint, like 45, goes up by convention: $45 \to 50$.

How to use

0 – 103.4

0.01

0

0.1

4

1

3

3.4 = 3 + 4×0.1 + 0×0.01

Expanded form · 0.01 / 0.1 / 1 / 10

Decimals round the same way

Look one place further right:

• $3.27$ to one decimal place: the next digit is 7, round up → $3.3$;
• $3.24$ to one decimal place: the next digit is 4, round down → $3.2$;
• $12.506$ to two decimal places: the next digit is 6, round up → $12.51$.

Rounding to a whole number means watching the tenths digit: $68.5 \to 69$, $68.4 \to 68$.

Rounding is not chopping

Chopping off trailing digits (called truncating) looks easier but always errs small: 47 chopped is 40, off by 7; rounded it is 50, off by only 3. Rounding lets its error fall on both sides, which is why it became the convention.

Stay sharp in real life: money usually has to be exact to the cent, not rounded to the dollar; "about 14 million" means the true figure wobbles somewhere between 13.95 and 14.05 million. Whenever you see "about", you are looking at a rounded number. Large approximations return in the next lesson, scientific notation.

Check yourself

Quick quiz

Try again

0 / 3 correct0 / 3 correct

1. 1. Round 438 to the nearest hundred.

   400440500

2. 2. Round 3.27 to one decimal place.

   3.23.33.25

3. 3. Round 68.5 to the nearest whole number.

   686968.5