Rounding and Estimating

What you will learn

• Round whole numbers to the nearest $10$, $100$ and $1000$.
• Use rounding to estimate an answer.
• Judge whether an answer is reasonable.

Before you start: you should know place value. See Place Value to a Million.

The idea

Sometimes an exact number is more than you need. “About $500$ people came” is easier to say and remember than ”$487$ people came”. Rounding swaps a number for a nearby one that is easier to work with, such as a multiple of $10$ or $100$.

Rounding to the nearest ten

On a number line, find the two tens on each side of your number. Pick the nearer one. The number $63$ sits between $60$ and $70$ and is nearer to $60$.

The rounding rule

You do not have to draw a line each time. Look at the digit just to the right of the place you are rounding to.

• If that digit is $0, 1, 2, 3$ or $4$, keep the place digit and round down.
• If it is $5, 6, 7, 8$ or $9$, add one to the place digit and round up.

Every digit after the rounding place becomes zero. So $4{,}572$ to the nearest hundred: look at the tens digit, $7$, round up to $4{,}600$.

Estimating

An estimate is a quick answer close to the real one. Round every number first, then do the sum with the rounded numbers. The symbol $\approx$ means “is about equal to”.

Estimating is a good check. If your exact answer is far from your estimate, you have probably made a mistake.

Worked examples

Example 1: Round to the nearest hundred

Round $6{,}351$ to the nearest hundred.

1. The hundreds digit is $3$ and the tens digit is $5$.
2. The tens digit is $5$ or more, so round up.
3. $3 + 1 = 4$ hundreds, and the rest become zeros.

Answer: $6{,}400$.

Example 2: Estimate a sum

Estimate $612 + 289$ by rounding to the nearest hundred.

1. $612 \approx 600$.
2. $289 \approx 300$.
3. $600 + 300 = 900$.

Answer: about $900$. (The exact answer is $901$.)

Example 3: Checking an answer

Is $52 \times 4 = 308$ reasonable?

1. Round $52$ to $50$.
2. $50 \times 4 = 200$.
3. $308$ is not close to $200$. The exact answer is $208$.

Answer: No. The estimate shows a mistake.

Rounding $9$ up in a place makes the digit before it go up by one. $397$ to the nearest ten is $400$, not $3{,}100$ or $300$.

Why it matters

People round all the time: prices, distances, populations and times. Estimating before you calculate is also the quickest way to catch errors, which is why the next lessons on column methods use it as a check.