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Question 1: Write each of the following numbers in figures:
(a) Fortyfive lakh, three thousand, six.
(b) Five crore, twentyone lakh, five thousand, seven hundred fortyseven.
(c) Twentyone crore, seventeen lakh, eightyone thousand, two hundred sixteen.
(d) Eightyfour crore, thirtysix thousand, nine hundred six.
(a) Fortyfive lakh, three thousand, six.
(b) Five crore, twentyone lakh, five thousand, seven hundred fortyseven.
(c) Twentyone crore, seventeen lakh, eightyone thousand, two hundred sixteen.
(d) Eightyfour crore, thirtysix thousand, nine hundred six.
Question 2: Arrange the following numbers in ascending order :
4,75,12,375; 26,75,30,275; 85,75,00,025; 12,76,878; 5,07,38,392
First we arrange the given numbers in the placevalue chart:
Out of the given numbers, two are 9digit numbers, two are 8digit numbers and one is a 7digit number.
In 9digit numbers, clearly 26,75,30,275 < 85,75,00,025
In 8digit numbers, clearly 4,75,12,375 < 5,07,38,392
Clearly, the 7digit number is the smallest.
So, 12,76,878 < 4,75,12,375 < 5,07,38,392 < 26,75,30,275 < 85,75,00,025
Hence, the given numbers in ascending order are:
12,76,878; 4,75,12,375; 5,07,38,392; 26,75,30,275; 85,75,00,025
Question 3: Write the following numbers in words :
(a) 23,58,954
(b) 5,03,94,681
(c) 8,59,24,639
(d) 54,38,74,094
Starting from the right, we make entries of the digits of each number in the
placevalue chart:
Question 4: Find the difference of the placevalues of the two 7s in 53,69,70,174.
Place value of 1st 7 from right (i.e., 7 at the tens place) = 7 × 10 = 70
Place value of 2nd 7 from right (i.e., 7 at the ten thousands place) = 7 × 10,000 = 70,000
Hence, difference of the placevalues = 70,000 – 70 = 69,930.
Question 5: Compare :
(a) 3,52,90,634 and 3,47,20,956
(b) 7,30,98,468 and 7,30,58,390
(a) Consider 3,52,90,634 and 3,47,20,956. Both are 8digit numbers. We start from
the leftmost digits.
Here, 3 = 3.
Next, we compare the second digits from the left.
Here, 5 > 4.
Thus, 3,52,90,634 > 3,47,20,956.
(b) Consider 7,30,98,468 and 7,30,58,390. Both are 8digit numbers.
7 = 7 (leftmost digits)
3 = 3 (second digits from the left)
0 = 0 (third digits from the left)
9 > 5 (fourth digits from the left)
Thus, 7,30,98,468 > 7,30,58,390
Question 6: Write each of the following numbers in figures :
(a) Three hundred seven thousand, eight hundred twentyone.
(b) Two million, seven hundred thirtyfour thousand, one hundred twelve.
(c) Fortyfive million, seven hundred ten thousand, twentynine.
(d) Nine hundred fortysix million, two thousand, four hundred twentyfive.
We can show the given numbers in the International placevalue chart as follows:
Hence, the required numbers in figures are :
(a) 307,821
(b) 2,734,112
(c) 45,710,029
(d) 946,002,425
Question 7: Write the number five crore, six lakh, ten thousand, nine hundred twentynine in figures.
We proceed as follows:
Step I: Make four periods as shown.
The first period from right will have three parts, second, third and fourth periods will have two parts each
Step II: Write all the crores in the first period from the left.
We fill all the parts, for example, if it is 5 crore, we write 05.Step III: Write all the lakhs in the second period from the left. Again we fill all the parts, for example, if it is 6 lakh, we write 06.
Step IV: Write all the thousands in the third period from the left.
Step V: Write the hundreds, tens and ones in the fourth period from the left.
Now, if the number begins with 0 on the extreme left, drop the zero.
Thus, five crore, six lakh, ten thousand, nine hundred twentynine is written as 5,06,10,929.
Question 8: Arrange the following numbers in descending order :
58,36,73,906; 8,46,36,318; 58,39,10,257; 87,66,879; 6,45,13,898
First we arrange the given numbers in the place value chart
Out of the given numbers, two are 9digit numbers, two are 8digit numbers and one is
a 7digit number.
In 9digit numbers, clearly 58,39,10,257 > 58,36,73,906.
In 8digit numbers, clearly 8,46,36,318 > 6,45,13,898.
Clearly, the 7digit number is the smallest.
So, 58,39,10,257 > 58,36,73,906 > 8,46,36,318 > 6,45,13,898 >87,66,879.
Hence, the given numbers arranged in descending order are:
58,39,10,257; 58,36,73,906; 8,46,36,318; 6,45,13,898; 87,66,879.
Question 9: Round off to the nearest ten :
(a) 73
(b) 145
(c) 295
(d) 3,244
(e) 51,766
(a) 73 when rounded off to the nearest 10 becomes 70.
(b) 145 becomes 150.
(c) 295 becomes 300. (Here, 9+1 =10, so 2 in the hundreds place becomes3)
(d) 3,244 becomes 3,240.
(e) 51,766 becomes 51,770.
From the above examples, we can say that, in order to round off a number to the nearest ten :
(a) We replace the digit in the ones place by 0.
(b) When the replaced digit is 5, 6, 7, 8 or 9, we increase the digit in the tens place by 1, otherwise we make no other change.
Question 10: Write the greatest and the smallest 7digit numbers (without repeating a digit) from the following digits :
(a) 4, 7, 6, 3, 1, 2 and 9
(b) 2, 5, 6, 4, 0, 3 and 7
(a) Arrange the given digits i.e., 4, 7, 6, 3, 1, 2 and 9 in descending order, we get 9764321. Thus, the greatest number is 97,64,321.
Similarly, by arranging the given digits in ascending order, we get the smallest number. Thus, the smallest number is 12,34,679.
(b) Similarly, greatest number is 76,54,320 and smallest number is 20,34,567
Question 11: Rewrite the following numbers using International placevalue system.
(a) Fifteen lakh, four thousand, twelve.
(b) Eight crore, ten lakh, six hundred twentynine.
(c) Thirtysix crore, five lakh, eleven thousand, two hundred forty.
Arrange the given numbers in Indian place valuechart.
Now, we can express the given numbers using the International placevalue chart.
(a) One million, five hundred four thousand, twelve.
(b) Eightyone million, six hundred twentynine.
(c) Three hundred sixty million, five hundred eleven thousand, two hundred forty.
Question 12: Find the successor of the :
(a) greatest 7digit number
(b) smallest 6digit number
(a) Greatest 7digit number is 99,99,999.
Thus, successor of 99,99,999 is 99,99,999 + 1 = 1,00,00,000.
(b) Smallest 6digit number is 1,00,000.
Thus, successor of 1,00,000 is 1,00,000 + 1 = 1,00,001.
Question 13: Round off to the nearest hundred :
(a) 263 (b) 1,350 (c) 4,731 (d) 5,660 (e) 32,892 (f) 53,960
(a) 263 becomes 300.
(b) 1,350 becomes 1,400.
(c) 4,731 becomes 4,700.
(d) 5,660 becomes 5,700.
(e) 32,892 becomes 32,900.
(f) 53,960 becomes 54,000 because 960 becomes 1,000 and 53,000 + 1,000 = 54,000.
From the above, we can say that in order to round off a number to the nearest hundred:
(a) We replace the tens and ones digits by 00.
(b) If the tens digit is 5 or greater than 5, we increase the digit in the hundreds place by 1, otherwise we make no other change.
Question 14: Write the placevalue of 7 in each of the following numbers :
(a) 2,73,49,008
(b) 75,92,54,164
(c) 30,05,97,214
Let us arrange the digits of the numbers in the placevalue chart.
(a) Placevalue of 7 in 2,73,49,008 = 7 × 10,00,000 = 70,00,000
(b) Placevalue of 7 in 75,92,54,164 = 7 × 10,00,00,000 = 70,00,00,000
(c) Placevalue of 7 in 30,05,97,214 = 7 × 1,000 = 7,000.
Question 15: Rewrite the following numbers using Indian placevalue system.
(a) Four million, three hundred fourteen thousand, five hundred fortyfive.
(b) Twentytwo million, sixtythree thousand, one hundred six.
(c) Four hundred twentyone million, six hundred eight thousand, four hundred seven.
Arrange the given numbers in the International placevalue chart.
Now, we can express the given numbers using Indian placevalue chart.
(a) Forty three lakh, fourteen thousand, five hundred fortyfive.
(b) Two crore, twenty lakh, sixtythree thousand, one hundred six.
(c) Fortytwo crore, sixteen lakh, eight thousand, four hundred seven.
Question 16: Write 54,73,92,510 in the expanded form.
Thus, 54,73,92,510 = 50,00,00,000 + 4,00,00,000 + 70,00,000 + 3,00,000 + 90,000 + 2,000 + 500 + 10 + 0
Question 17: Find the predecessor of the:
(a) Smallest 9digit number.
(b) Greatest 7digit number.
(a) Smallest 9digit number is 10,00,00,000.
Thus, predecessor of 10,00,00,000 is 10,00,00,000 – 1 = 9,99,99,999.
(b) Greatest 7digit number is 99,99,999.
Thus, predecessor of 99,99,999 is 99,99,999 – 1 = 99,99,998.
Question 18: Round off to the nearest thousand:
(a) 971 (b) 3,501 (c) 8,489 (d) 29,604 (e) 5,99,512
(a) 971 becomes 1,000.
(b) 3,501 becomes 4,000.
(c) 8,489 becomes 8,000.
(d) 29,604 becomes 30,000 because 29 + 1 = 30.
(e) 5,99,512 becomes 6,00,000 because 599 + 1 = 600.
From the above we can say that in order to round off a number to the nearest thousand:
(a) We replace the hundreds, tens and ones digits by 000.
(b) If the hundreds digits is 5 or greater than 5, we increase the digit in the thousands place by 1, otherwise we make no other change.
Rounding off to the nearest ten thousand or lakh or even greater place can be done following the similar line of action.
Question 19: Write the greatest and the smallest 8digit numbers using all the following digits (you may repeat the digits) :
7, 2, 0, 1, 8, 3, 4
The greatest number is 8,87,43,210.
The smallest number is 1,00,23,478.
Question 20: Using the International placevalue system, write the number names for each of the following numbers:
(a) 251,964 (b) 1,085,739 (c) 18,923,584 (d) 309,754,318
Let us arrange the digits in the International placevalue chart.
(a) Two hundred fiftyone thousand, nine hundred sixtyfour.
(b) One million, eightyfive thousand, seven hundred thirtynine.
(c) Eighteen million, nine hundred twentythree thousand, five hundred eightyfour.
(d) Three hundred nine million, seven hundred fiftyfour thousand, three hundred eighteen.
Question 21: Which is greater?
(a) 5,73,89,204 or 75,29,301
(b) 9,20,01,473 or 54,21,73,480
(a) 5,73,89,204 has 8 digits and 75,29,301 has 7 digits.
Thus, 5,73,89,204 > 75,29,301 or 75,29,301 < 5,73,89,204.
(b) 9,20,01,473 has 8 digits and 54,21,73,480 has 9 digits.
Thus, 54,21,73,480 > 9,20,01,473 or 9,20,01,473 < 54,21,73,480.
Question 22: A 3digit number was rounded off to the nearest hundred and the result was 600. Find the interval of the original number.
Each of the numbers from 550 to 599 can be rounded off as 600.
Also, each of the numbers from 601 to 649 can be rounded off as 600.
Thus, interval of the original number is 550 to 649.
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