Exact and Approximate Values – Rounding and Estimation of Large Numbers

Theory: In real life, we often use approximate numbers instead of exact values. Approximate numbers are useful for estimation, planning, and when precision is not required.
Example:
Question: The population of Chintamani is 76,068. Estimate it to the nearest thousand.
Solution: 76,068 ≈ 76,000

Theory: Rounding is helpful in planning, budgeting, and everyday conversations. It simplifies numbers for easier communication.
Example:
Question: A principal needs to order sweets for 732 students. Should they round up or down?
Solution: Round up to 750 to ensure enough sweets.

Theory: Rounding up means estimating to the next higher value; rounding down means estimating to the next lower value. The choice depends on the context.
Example:
Question: If an item costs ₹470, a shopkeeper may say it is around ₹450. What kind of rounding is this?
Solution: Rounding down.

Theory: Estimation helps in checking the reasonableness of addition and subtraction results. It’s useful in mental math.
Example:
Question: Estimate 4,63,128 + 4,19,682.
Solution: Estimate ≈ 4,60,000 + 4,20,000 = 8,80,000

Theory: Large numbers can be estimated to the nearest thousand, lakh, or crore by rounding according to digit positions.
Example:
Question: Find nearest lakh of 6,72,85,183.
Solution: Nearest lakh ≈ 6,73,00,000

Theory: Census and city data often require rounding for general public reporting and comparative studies.
Example:
Question: If Bengaluru’s population was 84,25,970 in 2011, round it to the nearest lakh.
Solution: 84,25,970 ≈ 84,00,000

Theory: Estimation gives a quick idea, but the actual value is needed for accuracy. Estimations can be checked against actual values.
Example:
Question: Is Estu’s estimate of 4,63,128 + 4,19,682 being close to 9,00,000 valid?
Solution: Actual = 8,82,810; Estu’s estimate (9,00,000) is a reasonable over-approximation.

Theory: Mental math with rounding helps in quick decision making. Round numbers to nearest ten, hundred, thousand for quick calculations.
Example:
Question: Estimate 14,63,128 – 4,90,020 by rounding each to nearest lakh.
Solution: ≈ 15,00,000 – 5,00,000 = 10,00,000

Theory: While estimation is useful, some situations require precise numbers like exams, official documents, financial statements, etc.
Example:
Question: Give an example where rounding is not acceptable.
Solution: Submitting tax forms or paying bills.

Theory: Estimation can be practiced using real-world comparisons like estimating travel time, crowd size, or object quantities to build number sense.
Example:
Question: Can Mumbai’s population (1.24 crore) fit into 1 lakh buses carrying 50 people each?
Solution: 1 lakh buses × 50 = 50 lakh < 124 lakh; No, it won’t fit.