NCERT Solutions Ganita Prakash (Part 1) Chapter 1 (Nearest Neighbours)1.4 Exact and Approximate Values — In-text Questions

Book page 11 Updated on2026-09-05

Q1.
Similarly, write the five nearest neighbours for these numbers: (a) 3,87,69,957 (b) 29,05,32,481
Answer

Look only at the digits to the right of the place you are rounding to: 5 or more rounds up, less than 5 rounds down.

Nearest…(a) 3,87,69,957(b) 29,05,32,481
thousand3,87,70,00029,05,32,000
ten thousand3,87,70,00029,05,30,000
lakh3,88,00,00029,05,00,000
ten lakh3,90,00,00029,10,00,000
crore4,00,00,00029,00,00,000
(a) last 3 digits 957 ≥ 500 → thousand rounds up to 3,87,70,000
last 4 digits 9957 ≥ 5000 → ten thousand also 3,87,70,000
last 5 digits 69,957 ≥ 50,000 → lakh up to 3,88,00,000
last 6 digits 7,69,957 ≥ 5,00,000 → ten lakh up to 3,90,00,000
last 7 digits 87,69,957 ≥ 50,00,000 → crore up to 4,00,00,000

(b) 481 < 500 → down; 2481 < 5000 → down; 32,481 < 50,000 → down;
5,32,481 ≥ 5,00,000 → up; 05,32,481 < 50,00,000 → down
Why it happens: Number (b) is interesting — four of its neighbours round down but the “nearest ten lakh” rounds up. That is because 5,32,481 is just past half of ten lakh, while 32,481 is well below half of a lakh. Each place is judged on its own.
Q2.
I have a number for which all five nearest neighbours are 5,00,00,000. What could the number be? How many such numbers are there?
Answer

The number must lie between 4,99,99,500 and 5,00,00,499, and there are exactly 1000 such whole numbers.

Nearest crore = 5,00,00,000 → number lies in 4,50,00,000 to 5,49,99,999
Nearest ten lakh = 5,00,00,000 → 4,95,00,000 to 5,04,99,999
Nearest lakh = 5,00,00,000 → 4,99,50,000 to 5,00,49,999
Nearest ten thousand = 5,00,00,000 → 4,99,95,000 to 5,00,04,999
Nearest thousand = 5,00,00,000 → 4,99,99,500 to 5,00,00,499

Count = 5,00,00,499 − 4,99,99,500 + 1 = 1000 numbers
Why it happens: Each condition is an interval around 5,00,00,000, and the intervals sit one inside the other — the crore condition is the loosest, the thousand condition the tightest. So the tightest one, the nearest-thousand band, decides everything, and every number inside it automatically satisfies the other four.
Check it yourself: Take 5,00,00,300. Nearest thousand = 5,00,00,000 ✓, nearest ten thousand = 5,00,00,000 ✓, nearest lakh, ten lakh and crore = 5,00,00,000 ✓. All five agree.
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