Hinglish

Exact and Approximate Values

Class 7 Maths · Chapter 1: Large Numbers Around Us · NCERT Ganita Prakash section 1.4

Learn

A newspaper says "1 lakh people visited the book fair." Did exactly 1,00,000 come? Probably not! Very often an approximate number is enough. If a town has 76,068 people, saying "about 76,000" (or even "about 75,000") gives a good idea of its size.

Round up or down? Round up when running short would be a problem: for 732 people at a school function, order sweets for 750. Round down for a quick rough figure: a ₹470 item is "around ₹450". And some things must be exact: money in a bank, a phone number, a medicine dose.

Nearest neighbours: for 6,72,85,183 the nearest thousand is 6,72,85,000, the nearest ten thousand 6,72,90,000, the nearest lakh 6,73,00,000, the nearest ten lakh 6,70,00,000 and the nearest crore 7,00,00,000. Rule: look at the digit just to the right of that place: 5 or more → up, less than 5 → down.

6,72,85,183 ≈ 6,73,00,000 (nearest lakh)

Estimating sums: is 4,63,128 + 4,19,682 more or less than 8,50,000? Round: about 4,60,000 + 4,20,000 = 8,80,000, so more. The exact answer is 8,82,810. Estimating first helps you catch mistakes: if you got 98,28,10, you would know something went wrong!

4,63,128 + 4,19,682 = 8,82,810 ≈ 8,80,000

Explore: round on the number line.

  1. Put the marker at 4,63,128 rounded to the nearest ten thousand.
  2. Put the marker at 4,87,500 rounded to the nearest ten thousand.
  3. Put the marker at 4,19,682 rounded to the nearest lakh.

Remember

  • Approximate values are often enough; some things (money, phone numbers, medicine) must be exact.
  • To round, look at the next digit to the right: 5 or more → up, less than 5 → down.

Quick check

What is 3,87,69,957 rounded to the nearest lakh?

  1. 3,88,00,000
  2. 3,87,00,000
  3. 3,90,00,000
  4. 4,00,00,000
Answer

3,88,00,000. The digit after the lakhs place is 6 (5 or more), so round up.

Think about it

A number's nearest thousand, ten thousand, lakh, ten lakh and crore are all 5,00,00,000. Give one such number.

One answer

Any number from 4,99,99,500 up to 5,00,00,499 works, for example 5,00,00,123. It must round to 5,00,00,000 at every place, even the nearest thousand, so it must be within 500 of 5 crore.

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.