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 |
|---|---|---|
| thousand | 3,87,70,000 | 29,05,32,000 |
| ten thousand | 3,87,70,000 | 29,05,30,000 |
| lakh | 3,88,00,000 | 29,05,00,000 |
| ten lakh | 3,90,00,000 | 29,10,00,000 |
| crore | 4,00,00,000 | 29,00,00,000 |
(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
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.