RS Aggarwal Class 5 Solutions Chapter 11 Rounding Numbers
Exercise 51
(1) Round off each of the following numbers to the nearest ten.
(a) 81 – 80
(b) 478 – 480
(c) 875 – 880
(d) 4232 – 4230
(e) 20306 – 20310
(f) 34898 – 34900
(g) 105413 – 105410
(h) 208979 – 208980
(2) Round off each of the following numbers to the nearest hundred.
(a) 415 – 400
(b) 891 – 900
(c) 5650 – 5700
(d) 7132 – 7100
(e) 16309 – 16300
(f) 48768 – 48800
(g) 110111 – 110100
(h) 218676 – 218700
(3) Round off each of the following numbers to the nearest thousand.
(a) 6367 – 6000
(b) 8710 – 9000
(c) 13492 – 13000
(d) 26505 – 27000
(e) 218925 – 219000
(f) 576396 – 577000
(g) 1035608 – 1036000
(h) 1867299 – 1867000
(4) Round off each of the following numbers to the nearest ten-thousand.
(a) 13670 – 10000
(b) 16745 – 20000
(c) 15892 – 20000
(d) 21987 – 20000
(e) 347126 – 350000
(f) 148259 – 150000
(g) 462789 – 460000
(h) 1570358 – 1570000
(5) Round of each of the following to the nearest lakh.
(a) 138964 – 100000
(b) 347589 – 300000
(c) 461308 – 500000
(d) 782615 – 800000
(e) 1054319 – 1100000
(f) 1407685 – 1400000
(g) 16970354 – 17000000
(h) 21352419 – 21400000
(6) Round off each of the following to the nearest ten lakh
(a) 1916423 – 2000000
(b) 234 7917 – 2000000
(c) 7156902 – 7000000
(d) 6719543 – 7000000
(e) 2532104 – 3000000
(f) 16380547 – 16000000
(g) 36524179 – 37000000
(h) 54036658 – 54000000
(7) Round off each of the following to the nearest Crore
(a) 62735913 – 60000000
(b) 36478609 – 40000000
(c) 95632417 – 100000000
(d) 70869785 – 70000000
(e) 83754876 – 80000000
(f) 107342310 – 110000000
(8) Fill in the blanks.
On rounding off 136472508 to the nearest
(a) ten, we get __________
(b) hundred, we get __________
(c) thousand, we get __________
(d) ten thousand, we get __________
(e) lakh, we get __________
(f) crore, we get __________
Solution:
(a) The given number is 136472508
Its digit at unit place is 8, which is more than 5
So, increase the tens digit by 1 and replace the ones digit by 0
Therefore, On rounding off 136472508 to the nearest ten is 136472510
(b) The given number is 136472508
The digit at tens place is 0, which is lower than 5
So, replace the tens digit and ones digit by 0 and keeps the other digits as they are.
Therefore, On rounding off 136472508 to the nearest hundred is 136472500
(c) The given number is 136472508
The digit at hundred place is 5
So increase the thousand digit by 1 and replace the hundred, tens and ones digit by 0.
Therefore, On rounding off 136472508 to the nearest thousand is 136472000
(d) The given number is 136472508
The digit at thousand place is 2, which is lower than 5
So, replace the thousand, hundred, tens and ones place digit by 0 and keep the other digit as they are.
Therefore, On rounding off 136472508 to the nearest ten thousand is 136470000
(e) The given number is 136472508
The digit at ten thousand place is 7, which is more than 5
So, increase the digit at lakh place by 1, and replace the digit at ten thousand, thousand, hundred, tens and ones place by 0
Therefore, On rounding off 136472508 to the nearest lakh is 136500000
(f) The given number is 136472508
The digit at ten lakh place is 6, which is more than 5
So, increase the digit at crore place by 1 and replace the digit at ten lakh, lakh, ten thousand, thousand, hundred, tens and ones place by 0.
Therefore, On rounding off 136472508 to the nearest crore is 140000000
(9) The population of an Indian state is 85642574, Write the population
(a) to the nearest crore
(b) to the nearest lakh
(c) to the nearest thousand
Solution:
(a) The population is 85642574
The digit at ten lakh place is 5.
So, increase the digit at crore place by 1 and replace the digit ten lakh, lakh, ten thousand, thousand, hundred, tens and ones place by 0
Therefore, the answer to the nearest crore is = 90000000
(b) The population is 85642574
The digit at ten thousand place is 4, which is lower than 5
So, replace the digit at ten thousand, thousand, hundred, tens and ones place by 0 and keep the remaining digit as they are.
Therefore, the answer to the nearest lakh is – 85600000
(c) The population is 85642574
The digit at hundred place is 5.
So, increase the digit at thousand place by 1, and replace the digit at hundred, tens and ones place by 0
Therefore, the answer to the nearest thousand is 856423000
(10) Think of rounding to the nearest ten, What numbers could be rounded to
(a) 70 – 65, 66, 67, 68, 69, 71, 72, 73, 74
(b) 140 – 135, 136, 137, 138, 139, 141, 142, 143, 144
(c) 990 – 985, 986, 987, 988, 989, 991, 992, 993, 994
(d) 2350 – 2345, 2356, 2347, 2348, 2349, 2351, 2352, 2353, 2354
(11) Think of rounding to the nearest hundred. What numbers could be rounded to
(a) 900 = 850 to 949
(b) 1600 = 1550 – 1649
(c) 5300 = 5250 – 5349
(d) 32500 = 32450 – 32549
(12) Think of rounding to the nearest thousand, What numbers could be rounded to
(a) 9000 = 8500 – 9499
(b) 18000 = 1750 – 18499
(c) 27000 = 26500 – 27499
Exercise 52
(1) Round off each of the following decimals to the nearest one.
(a) 6.3
The given decimal is 6.3
Its digit at the 1st decimal place is 3, which is less than 5.
So replace each digit after the decimal point by 0.
Therefore, round off of 6.3 is 6.0
(b) 2.7
The given decimal is 2.7
Its digit at the 1st decimal place is 7, which is more than 5
So, increase the digit at ones place by 1 and replace the each digit after the decimal point by 0.
Therefore round off of 2.7 is 3.0
(c) 4.5
The given decimal is 4.5
Its digit at the 1st decimal place is 5
So, increase the digit at ones place by 1 and replace the digit after the decimal point by 0.
Therefore, rounding off of 4.5 is 5.0
(d) 16.8
The given decimal is 16.8
Its digit at the 1st decimal place is 8, which is more than 5
So, increase the digit at ones place by 1 and replace the digit after the decimal point by 0.
Therefore, rounding off of 16.8 is 17.0
(e) 13.64
The given decimal is 13.64
Its digit at the 1st decimal place is 6, which is more than 5
So, increase the digit at unit place by 1 and replace each digit after the decimal point by 0.
Therefore, rounded off of 13.64 is 14.00
(f) 37.532
The given decimal is 37.532
Its digit at the 1st decimal is 5,
So, increase the digit at unit place by 1 and replace each digit after the decimal point by 0
Therefore, rounding off of 37.532 is 38.000
(g) 10.05
The given decimal is 10.05
Its digit at the 1st decimal place is 0, which is lower than 5
So, replace each digit after the decimal point by 0.
Therefore, rounded off of 10.05 is 10.00
(h) 76.703
The given decimal is 76.703
Its digit at the 1st decimal place is 7, which is more than 5
So increase the digit at unit place by 1 and replace each digit after the decimal point by 0
Therefore, rounded off of 76.703 is 77.000
(2) Write each of the following decimals correct to one decimal place
(a) 3.74
The given decimal is 3.74
Its digit at the 2nd decimal place is 4, which less than 5
So, we replace every digit after the 1st decimal place by 0
Answer: 3.70
(b) 8.36
The given decimal is 8.36
Its digit at the 2nd decimal place is 6, which is more than 5
So, increase the digit at the 1st decimal place by 1 and replace each digit after it by 0
Answer: 8.40
(c) 9.65
The given decimal is 9.65
Its digit at the 2nd decimal place is 5
So, increase the digit at the 1st decimal place by 1 and replace each digit after the decimal point by 0
Answer: 9.70
(d) 10.347
The given decimal is 10.347
Its digit at the 2nd decimal place is 4, which is less than 5
So, we replace each digit after the 1st decimal place by 0.
Answer: 10.300
(e) 24.829
The given decimal is 24.829
Its digit at the 2nd unit place is 2, which is lower than 5
So, we replace each digit after the 1st decimal place by 0.
Answer: 24.800
(f) 32.271
The given decimal is 32.271
Its digit at the 2nd unit place is 7 which is greater than 5.
So, increase the digit at the 1st decimal place by 1 and replace each digit after the decimal point by 0
Ans. 32.300
(g) 86.813
The given decimal is 86.813
Its digit at the 2nd unit place is 1, which is lower than 5
So, we replace each digit after the 1st decimal place by 0.
Answer. 86.800
(h) 102.382
The given decimal is 102.382
Its digit at the 2nd unit place is 8 which is greater than 5.
So, increase the digit at the 1st decimal place by 1 and replace each digit after the decimal point by 0
Ans. 102.300
(3) Write each of the following decimals correct to two decimal place.
(a) 0.706
The given decimal is 0.706
Its digit at the 3rd decimal place is 6, which is more than 5
So, increase the digit at 2nd decimal place by 1 and replace each digit after it by 0
So, the answer is 0.710
(b) 5.238
The given decimal is 5.238
Its digit at the 3rd decimal place is 8, which is more than 5
So, increase the digit at 2nd decimal place by 1 and replace each digit after it by 0
So, the answer is 5.240
© 11.415
The given decimal is 11.415
Its digit at the 3rd decimal place is 5
So, increase the digit at 2nd decimal place by 1 and replace each digit after it by 0
So, the answer is 11.420
(d) 17.893
The given decimal is 17.893
Its digit at the 3rd decimal place is 3, which is lower than 5
So, replace each digit at the 3rd decimal place and onward by 0.
So, the answer is 17.890
(e) 26.682
The given decimal is 26.682
Its digit at the 3rd decimal place is 2, which is lower than 5
So, replace each digit at the 3rd decimal place and onward by 0.
So, the answer is 26.680
(f) 47.8491
The given decimal is 47.8491
Its digit at the 3rd decimal place is 9, which is more than 5
So, increase the digit at 2nd decimal place by 1 and replace each digit after it by 0
So, the answer is 47.8500
(g) 53.1475
The given decimal is 53.1475
Its digit at the 3rd decimal place is 7, which is more than 5
So, increase the digit at 2nd decimal place by 1 and replace each digit after it by 0
So, the answer is 53.1500
(h) 103.7651
The given decimal is 103.7651
Its digit at the 3rd decimal place is 5
So, increase the digit at 2nd decimal place by 1 and replace each digit after it by 0
So, the answer is 103.7700
(4) Write each of the following decimals correct to the three decimal places.
(a) 0.7894
The given decimal is 0.7894
Its digit at the 4th decimal place is 4, which is lower than 5
So, replace each digit at the 4th decimal place and onward by 0.
So, the answer is 0.7890
(b) 2.1635
The given decimal is 2.1635
Its digit at the 4th decimal place is 5
So, increase the digit at 3rd decimal place by 1 and replace each digit after it by 0
So, the answer is 2.1640
(c) 78.4728
The given decimal is 78.4728
Its digit at the 4th decimal place is 8
So, increase the digit at 3rd decimal place by 1 and replace each digit after it by 0
So, the answer is 78.4730
(d) 19.01472
The given decimal is 19.01472
Its digit at the 4th decimal place is 8
So, increase the digit at 3rd decimal place by 1 and replace each digit after it by 0
So, the answer is 78.4730
(e) 32.40361
The given decimal is 32.40361
Its digit at the 4th decimal place is 6
So, increase the digit at 3rd decimal place by 1 and replace each digit after it by 0
So, the answer is 32.40400
(f) 123.00416
The given decimal is 123.00416
Its digit at the 4th decimal place is 1, which is lower than 5
So, replace each digit at the 4th decimal place and onward by 0.
So, the answer is 123.00400
(5) Find the quotient correct to two decimal places in each of the following division sums.
(a) 2.3 / 9
= 0.2555
= 0.26
(b) 21.83 / 16
= 1.364
= 1.36
(c) 3.7 / 17
= 0.217
= 0.22
(d) 8.283 / 22
= 0.376
= 0.38
(e) 16.46 / 15
= 1.097
= 1.10
(f) 101.37 / 20
= 5.068
= 5.07
(6) Express each of the following fractions as decimal correct to 3 decimal places.
(a) 5/13
= 0.3846
= 0.385
(b) 6/7
= 0.8571
= 0.857
(c) 5/11
= 0.4545
= 0.456
(d) 6/13
= 0.4615
= 0.462
(e) 13/15
= 0.8666
= 0.867
(f) 3 4/11
= 3.3636
= 3.364
(g) 2 12/17
= 2.7058
= 2.706
(h) 10 2/3
= 10.6666
= 10.667
(7) Think of rounding to the nearest one. What numbers could be rounded to?
(a) 11.0 – greater than 10.5 and less than 11.5
(b) 17.0 – greater than 16.5 and less than 17.5
(c) 20.0 – greater than 19.5 and less than 20.5
(d) 46.0 – greater than 45.5 and less than 46.5.