Round off (approximate) each of the following to the nearest ten:
(i) 62
(ii) 265
(iii) 543
(iv) 6296
Answer
To round off to the nearest ten, look at the ones digit. If it is less than 5, replace it by 0; if it is 5 or more, increase the tens digit by 1 and replace the ones digit by 0.
(i) 62 → ones digit is 2 (less than 5) → 60.
(ii) 265 → ones digit is 5 → 270.
(iii) 543 → ones digit is 3 (less than 5) → 540.
(iv) 6296 → ones digit is 6 (more than 5) → 6300.
Round off (approximate) each of the following to the nearest hundred:
(i) 748
(ii) 784
(iii) 6998
(iv) 59997
Answer
To round off to the nearest hundred, look at the tens digit. If it is less than 5, replace the tens and ones digits by 0; if it is 5 or more, increase the hundreds digit by 1 and replace the tens and ones digits by 0.
(i) 748 → tens digit is 4 (less than 5) → 700.
(ii) 784 → tens digit is 8 (more than 5) → 800.
(iii) 6998 → tens digit is 9 (more than 5) → 7000.
(iv) 59997 → tens digit is 9 (more than 5) → 60000.
Round off (approximate) each of the following to the nearest thousand:
(i) 6475
(ii) 6732
(iii) 9948
(iv) 89994
Answer
To round off to the nearest thousand, look at the hundreds digit. If it is less than 5, replace the hundreds, tens and ones digits by 0; if it is 5 or more, increase the thousands digit by 1 and replace the digits on its right by 0.
(i) 6475 → hundreds digit is 4 (less than 5) → 6000.
(ii) 6732 → hundreds digit is 7 (more than 5) → 7000.
(iii) 9948 → hundreds digit is 9 (more than 5) → 10000.
(iv) 89994 → hundreds digit is 9 (more than 5) → 90000.
Round off (approximate):
(i) 578 to the nearest ten.
(ii) 578 to the nearest hundred.
(iii) 4327 to the nearest thousand.
(iv) 32974 to the nearest ten thousand.
(v) 27487 to the nearest ten thousand.
Answer
(i) To round off 578 to the nearest ten, look at the ones digit. It is 8 (more than 5), so increase the tens digit by 1 and replace the ones digit by 0.
Hence, 578 to the nearest ten = 580.
(ii) To round off 578 to the nearest hundred, look at the tens digit. It is 7 (more than 5), so increase the hundreds digit by 1 and replace the tens and ones digits by 0.
Hence, 578 to the nearest hundred = 600.
(iii) To round off 4327 to the nearest thousand, look at the hundreds digit. It is 3 (less than 5), so replace the hundreds, tens and ones digits by 0 and keep the other digit as it is.
Hence, 4327 to the nearest thousand = 4000.
(iv) To round off 32974 to the nearest ten thousand, look at the thousands digit. It is 2 (less than 5), so replace the thousands, hundreds, tens and ones digits by 0 and keep the other digit as it is.
Hence, 32974 to the nearest ten thousand = 30000.
(v) To round off 27487 to the nearest ten thousand, look at the thousands digit. It is 7 (more than 5), so increase the ten thousands digit by 1 and replace the digits on its right by 0.
Hence, 27487 to the nearest ten thousand = 30000.
Round off (approximate) each of the following to the nearest ten, nearest hundred and nearest thousand.
(i) 864
(ii) 1249
(iii) 54,547
(iv) 68,076
(v) 56,293
(vi) 7,293
(vii) 89,24,379
Answer
For the nearest ten, look at the ones digit; for the nearest hundred, look at the tens digit; for the nearest thousand, look at the hundreds digit. If that digit is less than 5, replace it (and the digits on its right) by 0; if it is 5 or more, increase the digit on its left by 1 and replace the digits on its right by 0.
(i) 864 :
Nearest ten → ones digit is 4 (less than 5) → 860. Nearest hundred → tens digit is 6 (more than 5) → 900. Nearest thousand → hundreds digit is 8 (more than 5) → 1000.
∴ 860, 900 and 1000.
(ii) 1249 :
Nearest ten → ones digit is 9 (more than 5) → 1250. Nearest hundred → tens digit is 4 (less than 5) → 1200. Nearest thousand → hundreds digit is 2 (less than 5) → 1000.
∴ 1250, 1200 and 1000.
(iii) 54,547 :
Nearest ten → ones digit is 7 (more than 5) → 54550. Nearest hundred → tens digit is 4 (less than 5) → 54500. Nearest thousand → hundreds digit is 5 (equal to 5) → 55000.
∴ 54550, 54500 and 55000.
(iv) 68,076 :
Nearest ten → ones digit is 6 (more than 5) → 68080. Nearest hundred → tens digit is 7 (more than 5) → 68100. Nearest thousand → hundreds digit is 0 (less than 5) → 68000.
∴ 68080, 68100 and 68000.
(v) 56,293 :
Nearest ten → ones digit is 3 (less than 5) → 56290. Nearest hundred → tens digit is 9 (more than 5) → 56300. Nearest thousand → hundreds digit is 2 (less than 5) → 56000.
∴ 56290, 56300 and 56000.
(vi) 7,293 :
Nearest ten → ones digit is 3 (less than 5) → 7290. Nearest hundred → tens digit is 9 (more than 5) → 7300. Nearest thousand → hundreds digit is 2 (less than 5) → 7000.
∴ 7290, 7300 and 7000.
(vii) 89,24,379 :
Nearest ten → ones digit is 9 (more than 5) → 8924380. Nearest hundred → tens digit is 7 (more than 5) → 8924400. Nearest thousand → hundreds digit is 3 (less than 5) → 8924000.
∴ 8924380, 8924400 and 8924000.
Approximate each of the following to the nearest ten:
(i) ₹ 562
(ii) 837 m
(iii) 545 cm
(iv) ₹ 27
Answer
To round off to the nearest ten, look at the ones digit. If it is less than 5, replace it by 0; if it is 5 or more, increase the tens digit by 1 and replace the ones digit by 0.
(i) ₹ 562 → ones digit is 2 (less than 5) → ₹ 560.
(ii) 837 m → ones digit is 7 (more than 5) → 840 m.
(iii) 545 cm → ones digit is 5 (equal to 5) → 550 cm.
(iv) ₹ 27 → ones digit is 7 (more than 5) → ₹ 30.
List all the natural numbers which can be rounded off to 30.
Answer
A number rounds off to 30 (to the nearest ten) when its ones digit decides whether it moves to 30 or away from it.
The numbers from 25 to 29 have ones digit 5 or more, so they round up to 30.
The numbers from 30 to 34 have ones digit less than 5, so they round down to 30.
Hence, the required numbers are 25, 26, 27, 28, 29, 30, 31, 32, 33 and 34.
List all the whole numbers which are approximate to 50.
Answer
A number rounds off to 50 (to the nearest ten) depending on its ones digit.
The numbers from 45 to 49 have ones digit 5 or more, so they round up to 50.
The numbers from 50 to 54 have ones digit less than 5, so they round down to 50.
Hence, the required numbers are 45, 46, 47, 48, 49, 50, 51, 52, 53 and 54.
Write the smallest and the largest numbers which are rounded off to 90.
Answer
A number rounds off to 90 (to the nearest ten) depending on its ones digit.
The numbers from 85 to 89 have ones digit 5 or more, so they round up to 90.
The numbers from 90 to 94 have ones digit less than 5, so they round down to 90.
So, the numbers that round off to 90 lie from 85 up to 94.
Hence, the smallest number is 85 and the largest number is 94.
Write the smallest and the largest numbers which are approximate to 130.
Answer
A number rounds off to 130 (to the nearest ten) depending on its ones digit.
The numbers from 125 to 129 have ones digit 5 or more, so they round up to 130.
The numbers from 130 to 134 have ones digit less than 5, so they round down to 130.
So, the numbers that round off to 130 lie from 125 up to 134.
Hence, the smallest number is 125 and the largest number is 134.