Rounding Decimals
Rounding decimals means approximating a decimal number to a specified place — the nearest whole number, nearest tenth, or nearest hundredth. Rounding makes numbers easier to work with and is used in estimation, money calculations, and measurement.
For example, if a pencil costs ₹7.85 and you want to estimate the cost of 12 pencils, you can round ₹7.85 to ₹8 and quickly estimate ₹96.
What is Rounding Decimals - Class 5 Maths (Decimals)?
- Identify the place to which you are rounding.
- Look at the digit to its right (the deciding digit).
- If the deciding digit is 5 or more, round up (increase the rounding digit by 1).
- If the deciding digit is less than 5, round down (keep the rounding digit as is).
- Drop all digits after the rounding place.
Rounding Decimals Formula
Deciding digit ≥ 5 → Round UP | Deciding digit < 5 → Round DOWN
Solved Examples
Example 1: Example 1: Round to nearest whole number
Problem: Round 7.83 to the nearest whole number.
Solution:
Rounding place: ones. Deciding digit: 8 (tenths).
8 ≥ 5 → round up: 7 → 8.
Answer: 7.83 ≈ 8
Example 2: Example 2: Round to nearest whole number (round down)
Problem: Round 12.34 to the nearest whole number.
Solution:
Deciding digit: 3 (tenths). 3 < 5 → round down.
Answer: 12.34 ≈ 12
Example 3: Example 3: Round to nearest tenth
Problem: Round 4.567 to the nearest tenth.
Solution:
Rounding place: tenths (5). Deciding digit: 6 (hundredths).
6 ≥ 5 → round up: 5 → 6.
Answer: 4.567 ≈ 4.6
Example 4: Example 4: Round to nearest hundredth
Problem: Round 9.2348 to the nearest hundredth.
Solution:
Rounding place: hundredths (3). Deciding digit: 4 (thousandths).
4 < 5 → round down.
Answer: 9.2348 ≈ 9.23
Example 5: Example 5: Rounding with the digit 5
Problem: Round 3.45 to the nearest tenth.
Solution:
Rounding place: tenths (4). Deciding digit: 5.
5 ≥ 5 → round up: 4 → 5.
Answer: 3.45 ≈ 3.5
Example 6: Example 6: Rounding that changes the ones digit
Problem: Round 6.97 to the nearest tenth.
Solution:
Rounding place: tenths (9). Deciding digit: 7.
7 ≥ 5 → round up: 9 → 10. Carry 1 to ones: 6 → 7.
Answer: 6.97 ≈ 7.0
Example 7: Example 7: Word problem — Shopping
Problem: Kavi buys vegetables weighing 2.847 kg. Round this to the nearest tenth of a kg.
Solution:
Rounding place: tenths (8). Deciding digit: 4.
4 < 5 → round down.
Answer: The weight is approximately 2.8 kg.
Example 8: Example 8: Word problem — Estimation
Problem: Aditi's test scores are 8.75, 9.23, 7.68, and 8.41. Round each to the nearest whole number and estimate the total.
Solution:
- 8.75 ≈ 9
- 9.23 ≈ 9
- 7.68 ≈ 8
- 8.41 ≈ 8
Estimated total = 9 + 9 + 8 + 8 = 34
Answer: Estimated total ≈ 34
Example 9: Example 9: Multiple rounding levels
Problem: Round 15.6789 to: (a) nearest tenth, (b) nearest hundredth, (c) nearest whole number.
Solution:
(a) Nearest tenth: deciding digit 7 → round up → 15.7
(b) Nearest hundredth: deciding digit 8 → round up → 15.68
(c) Nearest whole: deciding digit 6 → round up → 16
Key Points to Remember
- Look at the digit immediately to the right of the rounding place.
- If this digit is 5 or more, round up. If less than 5, round down.
- Drop all digits after the rounding place.
- Rounding to the nearest tenth means keeping one decimal place.
- Rounding to the nearest hundredth means keeping two decimal places.
- Sometimes rounding up causes the rounding digit to become 10, requiring carrying to the next place.
- Rounding is an approximation — the rounded value is close to but not exactly equal to the original.
Practice Problems
- Round 45.678 to the nearest whole number.
- Round 3.142 to the nearest tenth.
- Round 8.995 to the nearest hundredth.
- Round 0.0567 to the nearest hundredth.
- The distance between two towns is 23.456 km. Round to the nearest tenth.
- Round each price to the nearest rupee: ₹15.72, ₹8.49, ₹23.50.
- Round 99.96 to the nearest tenth.
- Estimate 4.78 + 3.21 + 7.95 by rounding each to the nearest whole number.
Frequently Asked Questions
Q1. What does rounding to the nearest tenth mean?
It means keeping only one digit after the decimal point. Look at the hundredths digit to decide whether to round up or down. For example, 3.47 rounds to 3.5 (7 ≥ 5) and 3.42 rounds to 3.4 (2 < 5).
Q2. What happens when I round 9.95 to the nearest tenth?
The tenths digit is 9, and the deciding digit (hundredths) is 5. Round up: 9 becomes 10, so carry 1 to the ones. 9.95 rounds to 10.0.
Q3. Is 3.50 the same as 3.5 after rounding?
Yes. 3.50 and 3.5 have the same value. The trailing zero does not change the number. However, in some contexts (like measurements), writing 3.50 shows precision to the hundredths place.
Q4. Why do we round decimals?
Rounding makes numbers easier to work with for estimation and mental maths. It is also used when exact precision is not needed, such as rounding money to the nearest rupee or distances to the nearest km.
Q5. How do I round to the nearest hundredth?
Keep two digits after the decimal point. Look at the third decimal digit (thousandths). If it is 5 or more, round the hundredths digit up. If less than 5, keep it as is.
Q6. Can rounding change the whole number part?
Yes. If the decimal is close to the next whole number, rounding up will change it. For example, 7.96 rounded to the nearest tenth is 8.0, and 99.7 rounded to the nearest whole is 100.
Q7. What is the difference between rounding and truncating?
Rounding considers the next digit to decide whether to go up or down. Truncating simply cuts off the extra digits. For example, 3.78 truncated to one decimal place is 3.7, but rounded it is 3.8.
Q8. Is rounding covered in Class 5 NCERT?
Yes. Rounding decimals is part of the Decimals chapter in Class 5 NCERT Maths. Students learn to round to the nearest whole number, tenth, and hundredth.
Related Topics
- Decimals (Grade 5)
- Rounding Large Numbers
- Comparing and Ordering Decimals
- Addition of Decimals
- Subtraction of Decimals
- Multiplication of Decimals
- Division of Decimals
- Converting Fractions to Decimals (Grade 5)
- Converting Decimals to Fractions
- Decimal Word Problems (Grade 5)
- Decimal Place Value (Grade 5)
- Multiplying Decimals by 10, 100 and 1000
