Round Decimals with a Number Line | Grade 5 Math | LevelKite

To round a number is to swap it for a nearby number that is simpler to use. The rounded number is not always exact, but it is always close.

Take $3.7$ . It is more than $3$ and less than $4$ , so $3$ and $4$ are its neighbours. The lower neighbour, $3$ , is the whole number just below it. The upper neighbour, $4$ , is the whole number just above it.

To round $3.7$ to the nearest whole number, you pick the neighbour that is nearer.

The number line below goes from $3$ to $4$ in steps of one tenth. Find the marker at $3.7$ and count the steps to each neighbour.

Back to $3$ : 7 steps. That is 7 tenths, or $0.7$ .
On to $4$ : 3 steps. That is 3 tenths, or $0.3$ .

Since $0.3 < 0.7$ , the number $3.7$ is nearer to $4$ . Rounded to the nearest whole number, $3.7$ is $4$ .

The marker at

3.7

is 7 steps from

3

and 3 steps from

4

. The marker at

3.5

is in the middle of the line.

You do not have to count steps every time. Look at the other marker on the line above, at $3.5$ . It shows the halfway point: the number exactly in the middle of the two neighbours. It is 5 steps from $3$ and 5 steps from $4$ .

The halfway point splits the line into two parts:

A number on this line that is less than $3.5$ is nearer to $3$ .
A number on this line that is more than $3.5$ is nearer to $4$ .

Since $3.7 > 3.5$ , you know that $3.7$ rounds to $4$ without counting a single step.

What about $3.5$ itself? It is just as far from $3$ as from $4$ , so neither neighbour is nearer. So that everyone gets the same answer, there is an agreed rule: a number at the halfway point rounds up, to the upper neighbour. So $3.5$ rounds to $4$ .

Worked example

Round to the nearest whole number

Round $6.35$ to the nearest whole number.

Find the neighbours. 6.35 has 6 ones and part of one more, so it is more than 6 and less than 7. Its neighbouring whole numbers are 6 and 7.
$6 < 6.35 \quad \text{and} \quad 6.35 < 7$
Find the halfway point, because it marks where nearer to 6 ends and nearer to 7 begins. The number exactly in the middle of 6 and 7 is 6.5. It is 5 tenths above 6 and 5 tenths below 7.
Compare 6.35 with the halfway point. Write 6.5 as 6.50 so that both numbers show hundredths. The ones match. In the tenths place, 3 is less than 5, so 6.35 is less than 6.50.
$6.35 < 6.50$
A number below the halfway point is nearer to the lower neighbour. So 6.35 rounds down, which means you choose the lower neighbour, 6. The number line after this example shows it: the marker at 6.35 is to the left of the marker at 6.5.

Answer

Rounded to the nearest whole number, $6.35$ is $6$ .

Each small step is 5 hundredths, so

6.35

is on the tick between

6.3

and

6.4

. It is to the left of the halfway point,

6.5

, so it is nearer to

6

.

Rounding to the nearest tenth works the same way. Only the neighbours change: now they are tenths, not whole numbers.

Take $4.72$ . Keep its digits as far as the tenths place and you get $4.7$ . That is the lower neighbour. One tenth more is $4.8$ , the upper neighbour. So $4.72$ lies between $4.7$ and $4.8$ . The halfway point between them is $4.75$ , which is 5 hundredths from each.

The number line below zooms in on just the part from $4.7$ to $4.8$ . Each step is one hundredth. From the marker at $4.72$ it is 2 steps back to $4.7$ and 8 steps on to $4.8$ . That is 2 hundredths against 8 hundredths.

Since $0.02 < 0.08$ , the number $4.72$ is nearer to $4.7$ . Rounded to the nearest tenth, $4.72$ is $4.7$ .

This line shows only the part from

4.7

to

4.8

. The marker at

4.72

is 2 steps from

4.7

and to the left of the halfway point,

4.75

.

Here is how to tell that $4.72$ is left of the halfway point without counting. Line up the two numbers:

halfway point: $4.75$
your number: $4.72$

The ones match and the tenths match. The numbers first differ in the hundredths place, which is one place to the right of the tenths place. The halfway point has a 5 there and your number has a 2. Since $2 < 5$ , your number is below the halfway point.

That one digit did all the work. The same thing happened with $6.35$ : its tenths digit, 3, is less than the 5 in $6.5$ .

Key concept

The digit to the right decides

The rounding place is the place you are rounding to. Rounding means choosing the nearer of the two neighbours at that place.

To see which neighbour is nearer, look at the digit one place to the right of the rounding place. The halfway point has a 5 there.

0, 1, 2, 3 or 4: the number is below the halfway point. Round to the lower neighbour. The digit in the rounding place stays the same.
5, 6, 7, 8 or 9: the number is at the halfway point or above it. Round to the upper neighbour. It has one more in the rounding place.

Either way, the rounded number has no digits after the rounding place.

Worked example

Round to the nearest tenth

Round $2.86$ to the nearest tenth.

Find the neighbours. The rounding place is the tenths place. Keep the digits of 2.86 as far as the tenths to get the lower neighbour, 2.8. One tenth more is the upper neighbour, 2.9.
$2.8 < 2.86 \quad \text{and} \quad 2.86 < 2.9$
Look one place to the right of the tenths place, because that digit shows which side of the halfway point the number is on. It is the hundredths digit, 6.
Compare that digit with 5. The halfway point, 2.85, has a 5 in the hundredths place. Since 6 is more than 5, the number 2.86 is above the halfway point.
$2.86 > 2.85$
A number above the halfway point is nearer to the upper neighbour, so round up to 2.9. The tenths digit goes from 8 to 9, and you write no hundredths digit.

Answer

Rounded to the nearest tenth, $2.86$ is $2.9$ .

Worked example

Round to the nearest hundredth

Round $7.465$ to the nearest hundredth.

Find the neighbours. The rounding place is the hundredths place. Keep the digits as far as the hundredths to get the lower neighbour, 7.46. One hundredth more is the upper neighbour, 7.47.
$7.46 < 7.465 \quad \text{and} \quad 7.465 < 7.47$
Look one place to the right, at the thousandths digit. It is 5. A 5 puts the number at the halfway point or above it. Here 7.465 is exactly the halfway point between 7.46 and 7.47.
A number at the halfway point rounds up, so choose the upper neighbour, 7.47. The hundredths digit goes from 6 to 7, and you write no thousandths digit.

Answer

Rounded to the nearest hundredth, $7.465$ is $7.47$ .

What to remember: rounding means choosing the nearer of two neighbours. The halfway point between the neighbours shows which one is nearer. The digit one place to the right of the rounding place tells you which side of the halfway point you are on: 0 to 4 means the lower neighbour, and 5 to 9 means the upper neighbour.

Next, you will decide which place to round to from what a situation needs, such as the nearest cent. You will also find rounding mistakes and fix them.