Round decimals to suitable whole, tenth, or hundredth values

Ontario Grade 7 Mathematics

Number

Grade 7 Mathematics · B1.6

Imagine measuring a ribbon and getting 8.46 cm. If you only need an estimate to the nearest tenth of a centimetre, writing every digit gives more detail than you need. Rounding gives a nearby value at a chosen place. In this lesson, you will round decimals to a whole number, a tenth, or a hundredth. The situation tells you how much detail is useful.

What you will learn

Identify the whole-number, tenths, and hundredths places in a decimal.
Round a decimal to a suitable whole number, tenth, or hundredth.
Use nearby values to explain why a rounded answer makes sense.

Start with place value

A decimal is a number with a decimal point. The digits to its right show parts of one whole. The first place to the right is the tenths place. The next place is the hundredths place. For example, in

6.38

, the

3

is in the tenths place and the

8

is in the hundredths place.

A whole number has no fractional part. Rounding to the nearest whole number means choosing the closest whole number. Rounding to the nearest tenth means keeping one digit after the decimal point. Rounding to the nearest hundredth means keeping two digits after the decimal point.

The place you are rounding to is the target place. The digit immediately to its right helps you decide whether to keep the target digit or raise it by one. This is the rounding digit.

Whole number: no digits after the decimal point.
Tenth: one digit after the decimal point.
Hundredth: two digits after the decimal point.

Use the rounding rule

First, find the target place. Look one place to its right. If that digit is

0

,

1

,

2

,

3

, or

4

, keep the target digit the same. If it is

5

,

6

,

7

,

8

, or

9

, increase the target digit by one. Then leave out the digits to the right of the target place.

For instance, when rounding to the nearest tenth, the hundredths digit decides what happens. When rounding to the nearest hundredth, the thousandths digit decides. A thousandth is the third digit after the decimal point.

A number line can help show why the rule works. The rounded value is one endpoint, and the next value at that place is the other endpoint. A number closer to one endpoint rounds to that endpoint. A value exactly halfway is treated as rounding up by the rule above.

0\text{–}4\rightarrow\text{keep};\quad 5\text{–}9\rightarrow\text{raise by }1

Check the digit immediately after the place you are rounding to.
Digits from $0$ to $4$ : keep the target digit.
Digits from $5$ to $9$ : raise the target digit by one.

Choose a suitable level of detail

Suitable means useful for the purpose. If a question asks for a whole-number estimate, rounding to a tenth would give extra detail. If a measurement needs to be recorded to the nearest hundredth, rounding to a whole number would remove too much detail.

Read the requested place carefully. “Nearest tenth” and “nearest hundredth” are different instructions. A rounded answer should show the digits needed for that place. For example, a whole-number answer has no decimal part, while a tenth answer has one digit after the decimal point.

Before you finish, check that the result is near the original number. Rounding changes the number by less than one step at the target place. A step is

1

for whole numbers,

0.1

for tenths, and

0.01

for hundredths.

Use the place requested by the question or the purpose of the estimate.
Check that the rounded value is close to the starting value.
Keep the answer at the requested level of detail.

A quick plan

Use this plan each time: name the target place, find the digit immediately to its right, apply the rule, and write the rounded value. If the target digit is a

9

and you need to raise it, regroup to the place on its left. For example, raising the tenths digit in

4.98

changes the value to

5.0

when rounding to a tenth.

Try saying the reason aloud: “I am rounding to the nearest . The next digit is , so I .” This keeps the place and the decision clear.

Name the target place before looking at the deciding digit.
Use the next digit to make one clear decision.
Check the written answer matches the requested place.

Worked example

Round to the nearest tenth

A ribbon is

8.46

cm long. Round its length to the nearest tenth of a centimetre.

Locate 8.46 between tenths

The labelled points show that 8.46 is closer to 8.5 than to 8.4.

Find the target place
Nearest tenth means keep one digit after the decimal point. In $8.46$ , the tenths digit is $4$ .
$8.\mathbf{4}6$
Check the next digit
The hundredths digit is $6$ . Since it is at least $5$ , raise the tenths digit from $4$ to $5$ .
$6\geq 5$
Write the rounded value
The length rounded to the nearest tenth is $8.5$ cm. This is close to $8.46$ cm and has one digit after the decimal point.
$8.46\approx 8.5$

Answer:

8.5

cm

Check: The result is between

8.4

and

8.6

, and

8.46

is closer to

8.5

.

Worked example

Round to the nearest hundredth

A container holds

12.738

L of water. Round the amount to the nearest hundredth of a litre.

Locate 12.738 between hundredths

The value 12.738 is closer to 12.74 than to 12.73.

Find the target place
Nearest hundredth means keep two digits after the decimal point. In $12.738$ , the hundredths digit is $3$ .
$12.7\mathbf{3}8$
Check the next digit
The thousandths digit is $8$ . Since it is at least $5$ , raise the hundredths digit from $3$ to $4$ .
$8\geq 5$
Write the rounded value
The amount rounded to the nearest hundredth is $12.74$ L. It has exactly two digits after the decimal point.
$12.738\approx 12.74$

Answer:

12.74

L

Check:

12.74

is very close to

12.738

and is written to the hundredths place.

Worked example

Round to the nearest whole number

A walking route is

6.52

km long. Give its length to the nearest whole kilometre.

Locate 6.52 between whole numbers

The midpoint is 6.5. Since 6.52 is beyond it, the nearest whole number is 7.

Find the target place
Nearest whole number means keep the ones digit, which is $6$ . The tenths digit immediately to its right is $5$ .
$\mathbf{6}.52$
Apply the rule
The tenths digit is $5$ , so raise the ones digit from $6$ to $7$ . The digits after the decimal point are not needed in a whole-number answer.
$5\geq 5$
State the result
The route is about $7$ km to the nearest whole kilometre. Since $6.52$ is just past halfway between $6$ and $7$ , this result makes sense.
$6.52\approx 7$

Answer:

7

km

Check:

6.52

is closer to

7

than to

6

.

Common mistakes and how to avoid them

Looking at the target digit instead of the digit to its right.

Correction: Keep the target digit, then check the next digit to decide whether to change it.

Rounding to the wrong place, such as giving tenths when the question asks for whole numbers.

Correction: Underline or name the requested place before you begin.

Keeping every digit after rounding.

Correction: Remove digits to the right of the target place. Write only the level of detail requested.

Changing the target digit when the next digit is less than

5

.

Correction: For a next digit from

0

to

4

, leave the target digit unchanged.

Lesson summary

Choose the place named in the question: whole number, tenth, or hundredth.
Look at the digit immediately to the right of that place.
Keep the target digit for a next digit from $0$ to CAD 4; raise it by one for a next digit from $5$ to CAD 9.
Check that the rounded answer is close to the original number and shows the requested detail.

Check your understanding

Question 1

What is

3.27

rounded to the nearest tenth?

$3.2$
$3.3$
$3.27$
$4.0$

Show answer and explanation

3.3

The tenths digit is

2

. The hundredths digit is

7

, so raise the tenths digit to

3

. The answer is

3.3

.

Question 2

What is

9.843

rounded to the nearest hundredth?

$9.84$
$9.85$
$9.8$
$9.843$

Show answer and explanation

9.85

The hundredths digit is

4

. The thousandths digit is

3

, so keep the

4

. Wait: that gives

9.84

, which is the correct answer.

Question 3

What is

14.6

rounded to the nearest whole number?

$14$
$15$
$14.6$
$16$

Show answer and explanation

15

The ones digit is

4

, and the tenths digit is

6

. Since

6

is at least

5

, raise

4

to

5

. The answer is

15

.

Key terms

Decimal: A number written with a decimal point to show a whole amount and parts of a whole.
Tenths place: The first place to the right of the decimal point.
Hundredths place: The second place to the right of the decimal point.
Target place: The place named in the rounding instruction.
Rounding digit: The digit immediately to the right of the target place. It decides whether the target digit stays the same or increases.

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About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 7 Mathematics, expectation B1.6. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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B1.6 · Round decimals to suitable whole, tenth, or hundredth values

Ontario Grade 7 Mathematics

Grade 7 Mathematics · B1.6

What you will learn

Start with place value

Use the rounding rule

Choose a suitable level of detail

A quick plan

Round to the nearest tenth

Round to the nearest hundredth

Round to the nearest whole number

Common mistakes and how to avoid them

Lesson summary

Check your understanding

Question 1

Question 2

Question 3

Key terms

Continue through Grade 7 Math

About this lesson and its review