041. Rounding Decimal Numbers

Learning Intentions

• To understand that rounding involves approximating a decimal number to fewer decimal places
• round decimals to a given number of decimal places

Pre-requisite Summary

• Understand the meaning of the decimal point
• Know the place value of digits after the decimal point: tenths, hundredths, thousandths
• Be able to compare decimal digits by place value
• Understand that an approximation is close to, but not always equal to, the exact value
• Know that rounding depends on the digit immediately to the right of the stated place value
• Recall that digits $0,1,2,3,4$ round down and digits $5,6,7,8,9$ round up

Worked Examples

Worked Example 1

a) Explain what it means to round the decimal $4.682$ to $1$ decimal place.
b) Round $4.682$ to $1$ decimal place.
c) State whether the rounded value is exact or approximate.

Worked Example 2

Round each decimal to the given number of decimal places:
a) $7.36$ to $1$ decimal place
b) $2.847$ to $2$ decimal places
c) $9.504$ to $2$ decimal places

Worked Example 3

Round each decimal to the given number of decimal places:
a) $5.7831$ to $2$ decimal places
b) $0.468$ to $1$ decimal place
c) $12.995$ to $2$ decimal places

Worked Example 4

Round each decimal to the nearest whole number and then to $1$ decimal place:
a) $6.49$
b) $3.85$

Problems

Problem 1

a) Explain what it means to round the decimal $3.457$ to $1$ decimal place.
b) Round $3.457$ to $1$ decimal place.
c) State whether the rounded value is exact or approximate.

Problem 2

Round each decimal to the given number of decimal places:
a) $8.24$ to $1$ decimal place
b) $6.931$ to $2$ decimal places
c) $4.506$ to $2$ decimal places

Problem 3

Round each decimal to the given number of decimal places:
a) $9.2764$ to $2$ decimal places
b) $0.852$ to $1$ decimal place
c) $15.994$ to $2$ decimal places

Problem 4

Round each decimal to the nearest whole number and then to $1$ decimal place:
a) $7.58$
b) $2.34$

Exercises

Understanding and Fluency

1. Round each decimal to $1$ decimal place:
   a) $4.27$
   b) $6.84$
   c) $9.05$

2. Round each decimal to $1$ decimal place:
   a) $3.99$
   b) $0.46$
   c) $12.73$

3. Round each decimal to $2$ decimal places:
   a) $5.286$
   b) $7.431$
   c) $9.995$

4. Round each decimal to $2$ decimal places:
   a) $0.678$
   b) $14.203$
   c) $3.455$

5. Round each decimal to the nearest whole number:
   a) $4.2$
   b) $8.7$
   c) $12.5$

6. Round each decimal as directed:
   a) $6.483$ to $1$ decimal place
   b) $2.718$ to $2$ decimal places
   c) $15.049$ to $1$ decimal place

Reasoning

7. Explain why $5.67$ rounds to $5.7$ to $1$ decimal place.

8. A student rounds $4.38$ to $1$ decimal place and gets $4.4$. Is this correct? Explain.

9. A student rounds $7.245$ to $2$ decimal places and gets $7.24$. Explain the mistake.

10. Explain why rounding a decimal gives an approximation rather than the exact value.

Problem-solving

11. A runner records a time of $12.684$ seconds. Round this time to $1$ decimal place.

12. A jug contains $3.457$ L of water. Round this amount to $2$ decimal places.

13. A price is $8.996. Round this amount to $2$ decimal places.

14. A piece of wood is $2.49$ m long. Round this length to the nearest whole metre.

15. A measurement is $15.372$ cm. Round it to $1$ decimal place and to $2$ decimal places.

Potential Misunderstandings

• Students may look at the wrong digit when rounding
• Students may round using the digit in the chosen place value instead of the digit to its right
• Students may think rounding gives an exact answer rather than an approximation
• Students may forget that digits $5$ or more round up
• Students may change digits that should stay the same when rounding
• Students may not understand that digits after the rounded place value are removed after rounding
• Students may confuse rounding to a whole number with rounding to decimal places

Next: 042. Adding and Subtracting Decimals