BASIC LEVEL
Problem 1: Rounding 698 352
The general rule for rounding is: look at the digit one place to the right of the place you’re rounding to.
- If that digit is 5 or greater (5, 6, 7, 8, 9), round up (add 1 to the digit in the place you’re rounding to).
- If that digit is less than 5 (0, 1, 2, 3, 4), round down (keep the digit in the place you’re rounding to the same).
- All digits to the right of the rounding place become zeroes.
(a) To the nearest 100
- Identify the hundreds place: the digit is 3.
- Look at the digit to its right (the tens place): it is 5.
- Since 5 is 5 or greater, round up the 3 to a 4.
- Replace the digits to the right (tens and ones) with zeroes.
698 352 rounded to the nearest 100 is 698 400
(b) To the nearest 1000
- Identify the thousands place: the digit is 8.
- Look at the digit to its right (the hundreds place): it is 3.
- Since 3 is less than 5, round down (keep the 8 as it is).
- Replace the digits to the right (hundreds, tens, and ones) with zeroes.
698 352 rounded to the nearest 1000 is 698 000
(c) To the nearest 10 000
- Identify the ten thousands place: the digit is 9.
- Look at the digit to its right (the thousands place): it is 8.
- Since 8 is 5 or greater, round up the 9. Rounding 9 up means it becomes 10, so you write down 0 and carry over 1 to the next place (the hundred thousands place: 6+1=7).
- Replace the digits to the right (thousands, hundreds, tens, and ones) with zeroes.
698 352 rounded to the nearest 10 000 is 700 000
Problem 2: Correcting 45.7395
The same rounding rules apply to decimals. You look at the digit after the place you need to correct to.
(a) To 1 decimal place
- Identify the first decimal place (tenths place): the digit is 7.
- Look at the digit to its right (the hundredths place): it is 3.
- Since 3 is less than 5, round down (keep the 7 as it is).
- Drop all digits after the first decimal place.
45.7395 corrected to 1 decimal place is 45.7
(b) To the nearest whole number
- Identify the whole number (ones place): the digit is 5.
- Look at the digit to its right (the first decimal place/tenths): it is 7.
- Since 7 is 5 or greater, round up the 5 to a 6.
- Drop all digits after the decimal point.
45.7395 corrected to the nearest whole number is 46
(c) To 3 decimal places
- Identify the third decimal place (thousandths place): the digit is 9.
- Look at the digit to its right (the ten-thousandths place): it is 5.
- Since 5 is 5 or greater, round up the 9. Rounding 9 up means it becomes 10, so you write down 0 and carry over 1 to the previous digit (the 3 in the hundredths place: 3+1=4).
- Drop all digits after the third decimal place.
45.7395 corrected to 3 decimal places is 45.740
(The final zero must be included to show it is correctly rounded to three decimal places.)
I see you’ve provided images for a new set of problems. I will solve all of them with proper steps and reasoning, putting the question directly before its corresponding solution.
INTERMEDIATE LEVEL
3. Rectangular Plot Calculations
Question: The dimensions of a rectangular plot of land are 28.3 m by 53.7 m. Find:
(i) the perimeter of the land, correct to the nearest 10 m,
(ii) the area of grass needed to fill up the entire plot of land, correct to the nearest 100 m2.
(i) Perimeter, correct to the nearest 10 m
Step 1: Calculate the exact perimeter (P).
The formula is P=2(l+w).
P=2(53.7 m+28.3 m)P=2(82.0 m)P=164.0 m
Step 2: Round 164.0 m to the nearest 10 m.
- The digit in the tens place is 6.
- The digit to its right (ones place) is 4.
- Since 4<5, round down (keep the 6).
- Replace digits to the right with zeroes.
The perimeter of the land, correct to the nearest 10 m, is 160 m
(ii) Area, correct to the nearest 100 m2
Step 1: Calculate the exact area (A).
The formula is A=l×w.
A=53.7 m×28.3 m
A=1520.51 m2
Step 2: Round 1520.51 m2 to the nearest 100 m2.
- The digit in the hundreds place is 5.
- The digit to its right (tens place) is 2.
- Since 2<5, round down (keep the 5).
- Replace digits to the right with zeroes.
The area of grass needed, correct to the nearest 100 m2, is 1500 m2
4. Rounding Off Measurements
Question: Round off:
(a) 4.918 m to the nearest 0.1 m,
(b) 9.71 cm to the nearest cm,
(c) 10.982 to the nearest hundredth,
(d) 6.489 kg to the nearest 1001 kg.
(a) 4.918 m to the nearest 0.1 m (tenths place)
- Rounding digit (tenths) is 9.
- Look right (hundredths): 1.
- Since 1<5, round down.
4.9 m
(b) 9.71 cm to the nearest cm (whole number)
- Rounding digit (ones) is 9.
- Look right (tenths): 7.
- Since 7≥5, round up (9 becomes 10).
10 cm
(c) 10.982 to the nearest hundredth
- Rounding digit (hundredths) is 8.
- Look right (thousandths): 2.
- Since 2<5, round down.
10.98
(d) 6.489 kg to the nearest 1001 kg (hundredths place)
- Rounding digit (hundredths) is 8.
- Look right (thousandths): 9.
- Since 9≥5, round up (8 becomes 9).
6.49 kg
ADVANCED LEVEL
5. Kiran’s Rounding Explanation
Question: Kiran says that 5192.3 is equal to 519 when rounded off to the nearest 10. She drops the ‘2’ because it is less than 5. Do you agree with her? Explain your answer.
Answer: No, I do not agree with Kiran.
Explanation:
- Rounding to the nearest 10 means keeping the value of the tens place. The rounding digit is 9.
- The digit to the right (the ones place) is 2. Since 2<5, the 9 should stay the same (round down).
- All digits to the right of the tens place must become $\mathbf{0}$s to maintain the number’s magnitude.
- 5192.3 rounded to the nearest 10 is 5190.
- Kiran’s answer of 519 is incorrect because she dropped the 2 entirely without replacing it with a 0, which incorrectly changed the place value of the other digits (making the 9 the ones digit instead of the tens digit).
6. Largest and Smallest Possible Values
Question: A country’s population was 5 077 000 in 2010. This value has been rounded to the nearest 1000. What are the largest and smallest possible values of the country’s population in 2010?
Reasoning: If a number is rounded to the nearest 1000, the true value can be ±500 from the rounded value.
Smallest Possible Value (Lower Bound)
The smallest number that rounds up to 5 077 000 is found by subtracting 500.
Smallest=5 077 000−500=5 076 500
Largest Possible Value (Upper Bound)
The largest number that rounds down to 5 077 000 is found by adding 499.
Largest=5 077 000+499=5 077 499
The smallest possible value is 5 076 500 and the largest is 5 077 499
7. Farhan’s Rounding Explanation
Question: Farhan says that 26.97 is equal to 27 when rounded off to 1 decimal place because he thinks that 27.0 is the same as 27. Do you agree with him? Explain your answer.
Answer: No, I do not agree with Farhan’s reasoning on the final form.
Explanation:
- When rounding 26.97 to 1 decimal place, the tenths digit is 9.
- The digit to the right is 7, so we round up the 9, which carries over to the 26, resulting in 27.
- Crucially, to show that the number has been rounded to 1 decimal place, the answer must be written as 27.0.
- While 27.0 and 27 are numerically equal, the instruction “to 1 decimal place” is about precision (significant figures). The format 27.0 correctly communicates the required level of precision, whereas 27 implies rounding to the nearest whole number.