Rounding decimal numbers
🎯 In this topic you will
- Round a number with 2 decimal places to the nearest whole number.
- Round a number with 2 decimal places to the nearest tenth.
🧠 Key Words
- nearest
- round
Show Definitions
- nearest: Closest in value to a given number or place value.
- round: To change a number to a simpler value that is close to it, based on a chosen place value.
🔢 Why We Round Numbers
Rounding makes it easier to describe and understand numbers. It is easier to understand that Usain Bolt ran 100 metres in less than 10 seconds than he ran 100 metres in 9.63 seconds.
❓ EXERCISES
$1.$ Round these decimals to the nearest whole number.
$4.09 \quad 7.89 \quad 2.55 \quad 7.45$
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$2.$ Leo bought a book costing $14.65$.
What is the cost of the book to the nearest dollar?
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$3.$ Which of these numbers rounds to $5$ when rounded to the nearest whole number?
$4.35 \quad 4.05 \quad 4.5 \quad 5.05 \quad 4.55 \quad 5.35 \quad 5.5 \quad 5.53$
Check your answers to questions $1$ to $3$ with your partner.
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$4.$ Round these numbers to the nearest tenth.
$4.52 \quad 7.81 \quad 2.35 \quad 9.07$
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$5.$ Which of these numbers rounds to $7.5$ when rounded to the nearest tenth?
$7.35 \quad 7.05 \quad 7.51 \quad 7.55 \quad 7.49 \quad 7.56 \quad 7.53$
Check your answers to questions $4$ and $5$ with your partner.
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$6.$ Correct all the statements that are false.
A.$3.04$ is $3$ when rounded to the nearest whole number and the nearest tenth.
B.$5.03$ is $5$ when rounded to the nearest whole number and $5.0$ when rounded to the nearest tenth.
C.$6.95$ is $7$ when rounded to the nearest whole number and $6.9$ when rounded to the nearest tenth.
Discuss your answers with your partner.
Make sure you explain the reasons you have given.
👀 Show answer
A is false. Correct statement: $3.04$ is $3$ when rounded to the nearest whole number and $3.0$ when rounded to the nearest tenth.
B is correct.
C is false. Correct statement: $6.95$ is $7$ when rounded to the nearest whole number and $7.0$ when rounded to the nearest tenth.
$7.$ Round these measures to the nearest tenth.
$55.55$ litres $12.22$ metres $35.45$ kilograms
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$8.$ Choose the smallest number from this list that rounds to $1$.
$0.55 \quad 0.99 \quad 1.9 \quad 1.45 \quad 0.5 \quad 1.05 \quad 0$
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$9.$ Jasper says, ‘$7.97$ is $8$ when rounded to the nearest whole number and is also $8$ when rounded to the nearest tenth.’
Is Jasper correct?
Explain your answer.
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🧠 Think like a Mathematician
The sides of a rectangle are measured in centimetres to 2 decimal places using a micrometer (an instrument for measuring length accurately).
The measurements are rounded to the nearest whole number. They are $5\text{ cm}$ and $6\text{ cm}$.
What is the smallest possible perimeter of the rectangle?
What is the largest possible perimeter of the rectangle?
Investigate the smallest and largest perimeters for other rectangles if the measurements have been rounded to the nearest centimetre.
Think about the smallest number with 2 decimal places that rounds to $5\text{ cm}$, then think about the largest number with 2 decimal places that rounds to $5\text{ cm}$. Do the same for $6\text{ cm}$.
👀 show answer
If a length rounds to $5\text{ cm}$ (nearest whole number) and was measured to 2 decimal places, it can be from $4.50\text{ cm}$ to $5.49\text{ cm}$.
If a length rounds to $6\text{ cm}$, it can be from $5.50\text{ cm}$ to $6.49\text{ cm}$.
Smallest possible perimeter:
Use the smallest possible sides: $4.50$ and $5.50$.
$P = 2(l+w)=2(4.50+5.50)=2(10.00)=20.00\text{ cm}$
Largest possible perimeter:
Use the largest possible sides: $5.49$ and $6.49$.
$P = 2(l+w)=2(5.49+6.49)=2(11.98)=23.96\text{ cm}$
General idea (for your investigation): If rounded whole-number side lengths are $a$ and $b$, then with 2 decimal place measurements the perimeter lies between $2\big((a-0.50)+(b-0.50)\big)$ and $2\big((a+0.49)+(b+0.49)\big)$.