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 round down and digits round up

Worked Examples

Worked Example 1

a) Explain what it means to round the decimal to decimal place.

b) Round to 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) to decimal place

b) to decimal places

c) to decimal places

Worked Example 3

Round each decimal to the given number of decimal places:

a) to decimal places

b) to decimal place

c) to decimal places

Worked Example 4

Round each decimal to the nearest whole number and then to decimal place:

a)

b)

Problems

Problem 1

a) Explain what it means to round the decimal to decimal place.

b) Round to 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) to decimal place

b) to decimal places

c) to decimal places

Problem 3

Round each decimal to the given number of decimal places:

a) to decimal places

b) to decimal place

c) to decimal places

Problem 4

Round each decimal to the nearest whole number and then to decimal place:

a)

b)

Exercises

Understanding and Fluency

Exercise 1.

Round each decimal to decimal place:

a)

b)

c)

Exercise 2.

Round each decimal to decimal place:

a)

b)

c)

Exercise 3.

Round each decimal to decimal places:

a)

b)

c)

Exercise 4.

Round each decimal to decimal places:

a)

b)

c)

Exercise 5.

Round each decimal to the nearest whole number:

a)

b)

c)

Exercise 6.

Round each decimal as directed:

a) to decimal place

b) to decimal places

c) to decimal place

Reasoning

Exercise 7.

Explain why rounds to to decimal place.

Exercise 8.

A student rounds to decimal place and gets . Is this correct? Explain.

Exercise 9.

A student rounds to decimal places and gets . Explain the mistake.

Exercise 10.

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

Problem-solving

Exercise 11.

A runner records a time of seconds. Round this time to decimal place.

Exercise 12.

A jug contains L of water. Round this amount to decimal places.

Exercise 13.

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

Exercise 14.

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

Exercise 15.

A measurement is cm. Round it to decimal place and to 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 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