Write the numeral for each of the following :
(i) Eight lakh five thousand twelve.
(ii) Thirteen lakh three thousand eight.
(iii) Three crore three lakh three thousand three.
(iv) Five crore twelve lakh eighteen.
(v) Nine crore nineteen lakh five thousand eight.
(vi) Six crore thirty five lakh nineteen thousand sixteen.
(vii) Eleven crore twenty two lakh thirty three thousand four hundred fifty.
Answer
(i) Eight lakh five thousand twelve: 8,05,012
(ii) Thirteen lakh three thousand eight: 13,03,008
(iii) Three crore three lakh three thousand three: 3,03,03,003
(iv) Five crore twelve lakh eighteen: 5,12,00,018
(v) Nine crore nineteen lakh five thousand eight: 9,19,05,008
(vi) Six crore thirty five lakh nineteen thousand sixteen: 6,35,19,016
(vii) Eleven crore twenty two lakh thirty three thousand four hundred fifty: 11,22,33,450
Write each of the following in words :
(i) 8,08,080
(ii) 15,07,063
(iii) 87,08,109
(iv) 2,14,05,063
(v) 3,03,03,103
(vi) 10,06,05,368
Answer
(i) 8,08,080: Eight lakh eight thousand eighty.
(ii) 15,07,063: Fifteen lakh seven thousand sixty-three.
(iii) 87,08,109: Eighty-seven lakh eight thousand one hundred nine.
(iv) 2,14,05,063: Two crore fourteen lakh five thousand sixty-three.
(v) 3,03,03,103: Three crore three lakh three thousand one hundred three.
(vi) 10,06,05,368: Ten crore six lakh five thousand three hundred sixty-eight.
Write the place value of 4 in 8,46,572.
Answer
Counting from the right in 8,46,572 :
2 is in the ones place.
7 is in the tens place.
5 is in the hundreds place.
6 is in the thousands place.
4 is in the ten thousands place.
Hence, the place value of 4 in 8,46,572 is 40,000.
Write the place value of 7 in 7,30,493.
Answer
Counting from the right in 7,30,493 :
3 is in the ones place.
9 is in the tens place.
4 is in the hundreds place.
0 is in the thousands place.
3 is in the ten thousands place.
7 is in the lakhs place.
Hence, the place value of 7 in 7,30,493 is 7,00,000.
Write the place value of 6 in 23,76,400.
Answer
Counting from the right in 23,76,400 :
0 is in the ones place.
0 is in the tens place.
4 is in the hundreds place.
6 is in the thousands place.
7 is in the ten thousands place.
3 is in the lakhs place.
2 is in the ten lakhs place.
Hence, the place value of 6 in 23,76,400 is 6,000.
Write the place value of 9 in 19,63,605.
Answer
Counting from the right in 19,63,605 :
5 is in the ones place.
0 is in the tens place.
6 is in the hundreds place.
3 is in the thousands place.
6 is in the ten thousands place.
9 is in the lakhs place.
1 is in the ten lakhs place.
Hence, the place value of 9 in 19,63,605 is 9,00,000.
Write the place value of 8 in 20,07,189.
Answer
Counting from the right in 20,07,189 :
9 is in the ones place.
8 is in the tens place.
1 is in the hundreds place.
7 is in the thousands place.
0 is in the ten thousands place.
0 is in the lakhs place.
2 is in the ten lakhs place.
Hence, the place value of 8 in 20,07,189 is 80.
Write the place value of 3 in 23,608.
Answer
Counting from the right in 23,608 :
8 is in the ones place.
0 is in the tens place.
6 is in the hundreds place.
3 is in the thousands place.
2 is in the ten thousands place.
Hence, the place value of 3 in 23,608 is 3,000.
Find the difference between the place-values of two sixes in 6,56,348.
Answer
In 6,56,348, counting from the right:
8 is in the ones place.
4 is in the tens place.
3 is in the hundreds place.
6 is in the thousands place.
So, its place value is 6 × 1,000 = 6,000.
5 is in the ten thousands place.
6 is in the lakhs place.
So, its place value is 6 × 1,00,000 = 6,00,000.
Difference between the place-values of two sixes in 6,56,348 = 6,00,000 - 6,000 = 5,94,000
Hence, the difference between the place-values of two sixes in 6,56,348 is 5,94,000.
Find the difference between the place-value and the face-value of 8 in the numeral 5,86,273.
Answer
In the numeral 5,86,273, the digit '8' is in the ten thousands place.
So, its place value is 8 × 10,000 = 80,000.
The face value of a digit is the digit itself.
So, the face value of '8' is 8.
Difference = Place-value - Face-value
Difference = 80,000 − 8
Difference = 79,992
Hence, the difference between the place-value and the face-value of 8 in the numeral 5,86,273 = 79,992.
Write each of the following in expanded form :
(i) 5,16,287
(ii) 13,25,694
(iii) 8,08,808
(iv) 64,72,319
(v) 1,36,04,107
(vi) 9,36,50,519
Answer
(i) Expanding,
5,16,287 = 5 × 1,00,000 + 1 × 10,000 + 6 × 1,000 + 2 × 100 + 8 × 10+ 7 × 1
= 5,00,000 + 10,000 + 6,000 + 200 + 80 + 7.
(ii) Expanding,
13,25,694 = 1 × 10,00,000 + 3 × 1,00,000 + 2 × 10,000 + 5 × 1,000 + 6 × 100 + 9 × 10 + 4 × 1
= 10,00,000 + 3,00,000 + 20,000 + 5,000 + 600 + 90 + 4.
(iii) Expanding,
8,08,808 = 8 × 1,00,000 + 0 × 10,000 + 8 × 1,000 + 8 × 100 + 0 × 10 + 8 × 1
= 8,00,000 + 8,000 + 800 + 8.
(iv) Expanding,
64,72,319 = 6 × 10,00,000 + 4 × 1,00,000 + 7 × 10,000 + 2 × 1,000 + 3 × 100 + 1 × 10 + 9 × 1
= 60,00,000 + 4,00,000 + 70,000 + 2,000 + 300 + 10 + 9.
(v) Expanding,
1,36,04,107 = 1 × 1,00,00,000 + 3 × 10,00,000 + 6 × 1,00,000 + 0 × 10,000 + 4 × 1,000 + 1 × 100 + 0 × 10 + 7 × 1
= 1,00,00,000 + 30,00,000 + 6,00,000 + 4,000 + 100 + 7.
(vi) Expanding,
9,36,50,519 = 9 × 1,00,00,000 + 3 × 10,00,000 + 6 × 1,00,000 + 5 × 10,000 + 0 × 1,000 + 5 × 100 + 1 × 10 + 9 × 1
= 9,00,00,000 + 30,00,000 + 6,00,000 + 50,000 + 500 + 10 + 9.
Write the number corresponding to :
(5 × 1,00,000) + (1 × 10,000) + (4 × 1,000) + (7 × 100) + (3 × 10) + (8 × 1).
Answer
To find the number corresponding to the expanded form, we will calculate each term and then sum them up:
5 × 1,00,000 = 5,00,000
1 × 10,000 = 10,000
4 × 1,000 = 4,000
7 × 100 = 700
3 × 10 = 30
8 × 1 = 8
Now, add these values together:
5,00,000 + 10,000 + 4,000 + 700 + 30 + 8 = 5,14,738
Hence, the number corresponding to the given expanded form is 5,14,738.
Write the number corresponding to :
(6 × 1,00,000) + (6 × 1,000) + (3 × 10) + (6 × 1).
Answer
To find the number corresponding to the expanded form, we will calculate each term and then sum them up:
6 × 1,00,000 = 6,00,000
6 × 1,000 = 6,000
3 × 10 = 30
6 × 1 = 6
Now, add these values together:
6,00,000 + 6,000 + 30 + 6 = 6,06,036
Hence, the number corresponding to the given expanded form is 6,06,036.
Write the number corresponding to :
(1 × 10,00,000) + (2 × 1,00,000) + (3 × 10,000) + (4 × 100) + (6 × 10) + (9 × 1).
Answer
To find the number corresponding to the expanded form, we will calculate each term and then sum them up:
1 × 10,00,000 = 10,00,000
2 × 1,00,000 = 2,00,000
3 × 10,000 = 30,000
4 × 100 = 400
6 × 10 = 60
9 × 1 = 9
Now, add these values together:
10,00,000 + 2,00,000 + 30,000 + 400 + 60 + 9 = 12,30,469
Hence, the number corresponding to the given expanded form is 12,30,469.
Write the number corresponding to :
(2 × 10,00,000) + (3 × 1,00,000) + (7 × 1,000) + (9 × 100) + (4 × 10) + (5 × 1).
Answer
To find the number corresponding to the expanded form, we will calculate each term and then sum them up:
2 × 10,00,000 = 20,00,000
3 × 1,00,000 = 3,00,000
7 × 1,000 = 7,000
9 × 100 = 900
4 × 10 = 40
5 × 1 = 5
Now, add these values together:
20,00,000 + 3,00,000 + 7,000 + 900 + 40 + 5 = 23,07,945.
Hence, the number corresponding to the given expanded form is 23,07,945.
Write the number corresponding to :
(9 × 10,00,000) + (8 × 1,000) + (8 × 100) + (8 × 1).
Answer
To find the number corresponding to the expanded form, we will calculate each term and then sum them up:
9 × 10,00,000 = 90,00,000
8 × 1,000 = 8,000
8 × 100 = 800
8 × 1 = 8
Now, add these values together:
90,00,000 + 8,000 + 800 + 8 = 90,08,808.
Hence, the number corresponding to the given expanded form is 90,08,808.
Write the successor of each of the following :
(i) 6,001
(ii) 1,099
(iii) 12,749
(iv) 2,19,708
(v) 62,399
Answer
(i) The successor of 6,001 is 6,001 + 1 = 6,002.
(ii) The successor of 1,099 is 1,099 + 1 = 1,100.
(iii) The successor of 12,749 is 12,749 + 1 = 12,750.
(iv) The successor of 2,19,708 is 2,19,708 + 1 = 2,19,709.
(v) The successor of 62,399 is 62,399 + 1 = 62,400.
Write the predecessor of each of the following numbers :
(i) 99
(ii) 1,305
(iii) 32,000
(iv) 1,65,000
Answer
(i) The predecessor of 99 is 99 - 1 = 98.
(ii) The predecessor of 1,305 is 1,305 - 1 = 1,304.
(iii) The predecessor of 32,000 is 32,000 - 1 = 31,999.
(iv) The predecessor of 1,65,000 is 1,65,000 - 1 = 1,64,999.
Write the whole number whose successor is :
(i) 100
(ii) 6,299
(iii) 71,650
(iv) 42,000
Answer
(i) The whole number whose successor is 100 is 100 − 1 = 99.
(ii) The whole number whose successor is 6,299 is 6,299 − 1 = 6,298.
(iii) The whole number whose successor is 71,650 is 71,650 − 1 = 71,649.
(iv) The whole number whose successor is 42,000 is 42,000 − 1 = 41,999.
Write the whole number whose predecessor is :
(i) 1,000
(ii) 3,189
(iii) 3,001
(iv) 8,000
(v) 9,999
Answer
(i) The whole number whose predecessor is 1,000 is 1,000 + 1 = 1,001.
(ii) The whole number whose predecessor is 3,189 is 3,189 + 1 = 3,190.
(iii) The whole number whose predecessor is 3,001 is 3,001 + 1 = 3,002.
(iv) The whole number whose predecessor is 8,000 is 8,000 + 1 = 8,001.
(v) The whole number whose predecessor is 9,999 is 9,999 + 1 = 10,000.
Write down three consecutive whole numbers succeeding 72,597.
Answer
The three consecutive whole numbers succeeding 72,597 are:
72,597 + 1 = 72,598
72,598 + 1 = 72,599
72,599 + 1 = 72,600
Hence, three consecutive whole numbers succeeding 72,597 are 72,598, 72,599 and 72,600.
Write down three consecutive whole numbers just preceding 5,10,001.
Answer
To find the three consecutive whole numbers just preceding 5,10,001, we subtract 1 repeatedly:
5,10,001 - 1 = 5,10,000
5,10,000 - 1 = 5,09,999
5,09,999 - 1 = 5,09,998
Hence, the three consecutive whole numbers just preceding 5,10,001 are 5,10,000, 5,09,999, and 5,09,998.
How many 6-digit numbers are there in all?
Answer
There are 6-digit numbers from 1,00,000 to 9,99,999, inclusive.
To find the total count, you can use the formula:
Total numbers = (Largest number) - (Smallest number) + 1
Largest 6-digit number = 9,99,999
Smallest 6-digit number = 1,00,000
Total 6-digit numbers = 9,99,999 − 1,00,000 + 1
Total 6-digit numbers = 8,99,999 + 1
Total 6-digit numbers = 9,00,000
Hence, there are 9,00,000 six-digit numbers in all.
Write the largest 8-digit number.
Answer
The largest 8-digit number is formed by placing the largest digit (9) in all eight positions.
Hence, the largest 8-digit number is 9,99,99,999.
Write the smallest 8-digit number.
Answer
The smallest 8-digit number is formed by placing the second smallest digit (1) in first position and smallest digit (0) in all remaining positions.
Hence, the smallest 8-digit number is 1,00,00,000.
Write all possible 2-digit numbers formed by the digits 3, 7 and 9, when repetition of digits is not allowed.
Answer
All possible 2-digit numbers formed by the digits 3, 7 and 9, when repetition of digits is not allowed are;
Starting with 3:
37
39
Starting with 7:
73
79
Starting with 9:
93
97
Hence, the possible 2-digit numbers are 37, 39, 73, 79, 93, 97.
Write all possible 3-digit numbers that can be formed by the digits 1, 3 and 7, using each digit only once in each number.
Answer
Starting with 1:
137
173
Starting with 3:
317
371
Starting with 7:
713
731
Hence, the possible 3-digit numbers are 137, 173, 317, 371, 713 and 731.
Write all possible 3-digit numbers that can be formed by the digits 9, 2 and 0, using each digit only once in each number.
Answer
When forming 3-digit numbers using the digits 9, 2, and 0, with each digit used only once, we must remember that a 3-digit number cannot start with 0.
If the hundreds digit is 9 : the remaining digits are 2 and 0.
Possible numbers: 920, 902
If the hundreds digit is 2 : the remaining digits are 9 and 0.
Possible numbers: 290, 209
Hence, the possible 3-digit numbers are 920, 902, 290, 209.
Write the smallest 4-digit number that can be formed by the digits 0, 1, 3 and 6, using each digit only once.
Answer
The first digit of a 4-digit number cannot be 0. So, the smallest available non-zero digit is 1.
Thousands place: 1
The remaining digits are 0, 3, and 6. To make the number as small as possible, arrange these remaining digits in ascending order: 0, 3, 6.
Hundreds place: 0
Tens place: 3
Units place: 6
Combining all the data, the smallest 4-digit number is 1036.
Hence, the smallest 4-digit number is 1036.
Write the greatest 4-digit number that can be formed by the digits 0, 2, 7 and 5, using each digit only once.
Answer
The given digits are: 0, 2, 7, 5.
Arranging them in descending order:
Largest digit: 7 (for the thousands place)
Next largest: 5 (for the hundreds place)
Next largest: 2 (for the tens place)
Smallest digit: 0 (for the units place)
Hence, the greatest 4-digit number that can be formed is 7520.
Write the smallest 4-digit number of four different digits.
Answer
The digits available are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Thousands digit: The smallest digit is 0, but a number cannot start with 0 if it's meant to be a 4-digit number. So, the smallest non-zero digit, which is 1, must be in the thousands place.
Current digits used: {1}
Hundreds digit: Now that 1 is used, the smallest remaining digit available is 0.
Current digits used: {1, 0}
Tens digit: With 1 and 0 used, the next smallest digit available is 2.
Current digits used: {1, 0, 2}
Units digit: With 1, 0, and 2 used, the next smallest digit available is 3.
Current digits used: {1, 0, 2, 3}
Combining these digits in order, the smallest 4-digit number with four different digits is 1023.
Hence, the smallest 4-digit number with four different digits is 1,023.
Write the greatest 4-digit number of four different digits.
Answer
The digits available are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Thousands digit: The largest digit is 9.
Current digits used: {9}
Hundreds digit: From the remaining digits, the next largest is 8.
Current digits used: {9, 8}
Tens digit: From the remaining digits, the next largest is 7.
Current digits used: {9, 8, 7}
Units digit: From the remaining digits, the next largest is 6.
Current digits used: {9, 8, 7, 6}
Combining these digits in order, the greatest 4-digit number with four different digits is 9876.
Hence, the greatest 4-digit number with four different digits is 9,876.