Number System Exercise 1.1 |

Number System Exercise 1.2 |

Number System Exercise 1.3 |

**Question 1:**

**Write the numeral for each of the following numbers:**

**(i) Nine thousand eighteen**

**(ii) Fifty-four thousand seventy-three**

**(iii) Three lakh two thousand five hundred six**

**(iv) Twenty lakh ten thousand eight**

**(v) Six crore five lakh fifty-seven**

**(vi) Two crore two lakh two thousand two hundred two**

**(vii) Twelve crore twelve lakh twelve thousand twelve**

**(viii) Fifteen crore fifty lakh twenty thousand sixty-eight**

**Solution:**

(i) Nine thousand eighteen = 9018

(ii) Fifty-four thousand seventy-three = 54073

(iii) Three lakh two thousand five hundred six = 302506

(iv) Twenty lakh ten thousand eight = 2010008

(v) Six crore five lakh fifty-seven = 60500057

(vi) Two crore two lakh two thousand two hundred two = 20202202

(vii) Twelve crore twelve lakh twelve thousand twelve = 121212012

(viii) Fifteen crore fifty lakh twenty thousand sixty-eight = 155020068

**Question 2:**

**Write each of the following numbers in words:**

**(i) 63,005 = Sixty-three thousand five**

**(ii) 7,07,075**

**(iii) 34,20,019**

**(iv) 3,05,09,012**

**(v) 5,10,03,604**

**(vi) 6,18,05,008**

**(vii) 19,09,09,900**

**(viii) 6,15,30,807**

**(ix) 6,60,60,060**

**Solution:**

(i) 63,005 = Sixty-three thousand five

(ii) 7,07,075 = Seven lakh seven thousand seventy-five

(iii) 34,20,019 = Thirty-four lakh twenty thousand nineteen

(iv) 3,05,09,012 = Three crore five lakh nine thousand twelve

(v) 5,10,03,604 = Five crore ten lakh three thousand six hundred four

(vi) 6,18,05,008 = Six crore eighteen lakh five thousand eight

(vii) 19,09,09,900 = Nineteen crore nine lakh nine thousand nine hundred

(viii) 6,15,30,807 = Six crore fifteen lakh thirty thousand eight hundred seven

(ix) 6,60,60,060 = Six crore sixty lakh sixty thousand sixty

**Question 3:**

**Write each of the following numbers in expanded form:**

**(i) 15,768**

**(ii) 3,08,927**

**(iii) 24,05,609**

**(iv) 5,36,18,493**

**(v) 6,06,06,006 **

**(vi) 9,10,10,510**

**Solution:**

(i) 15,768 = (1 x 10000) + (5 x 1000) + (7 x 100) + (6 x 10) + (8 x 1)

(ii) 3,08,927 = (3 x 100000) + (8 x 1000) + (9 x 100) + (2 x 10) + (7 x 1)

(iii) 24,05,609 = (2 x 1000000) + (4 x 100000) + (5 x 1000) + (6 x 100) + (9 x 1)

(iv) 5,36,18,493 = (5 x 10000000) + (3 x 1000000) + (6 x 100000) + (1 x 10000) + (8 x 1000) + (4 x 100) + (9 x 10) + (3 x 1)

(v) 6,06,06,006 = (6 x 10000000) + (6 x 100000) + (6 x 1000) + (6 x 1)

(vi) 9,10,10,510 = (9 x 10000000) + (1 x 1000000) + (1 x 10000) + (5 x 100) + (1 x 10)

**Question 4:**

**Write the corresponding numeral for each of the following:**

**(i) 6 x 10000 + 2 x 1000 + 5 x 100 + 8 x 10 + 4 x 1**

**(ii) 5 x 100000 + 8 x 10000 + 1 x 1000 + 6 x 100 + 2 x 10 + 3 x1**

**(iii) 2 x 10000000 + 5 x 100000 + 7 x 1000 + 9 x 100 + 5 x 1**

**(iv) 3 x 1000000 + 4 x 100000 + 6 x 1000 + 5 x 100 + 7 x 1**

**Solution:**

(i) 6 x 10000 + 2 x 1000 + 5 x 100 + 8 x 10 + 4 x 1 = 62,584

(ii) 5 x 100000 + 8 x 10000 + 1 x 1000 + 6 x 100 + 2 x 10 + 3 x1 = 5,81,623

(iii) 2 x 10000000 + 5 x 100000 + 7 x 1000 + 9 x 100 + 5 x 1 = 2,05,07,905

(iv) 3 x 1000000 + 4 x 100000 + 6 x 1000 + 5 x 100 + 7 x 1 = 34,06,507

**Question 5:**

**Find the difference between the place values of the two nines in 79520986.**

**Solution:**

The place value of 9 at ten lakhs place = 90 lakhs = 9000000

The place value of 9 at hundreds place = 9 hundreds = 900

Therefore, Required difference = (9000000 – 900) = 8999100

**Question 6:**

**Find the difference between the place value and the face value of 7 in 27650934.**

**Solution:**

The place value of 7 in 27650934 = 70 lakhs = 70,00,000

The face value of 7 in 27650934 = 7

Therefore, Required difference = (7000000 – 7) = 69,99,993

**Question 7:**

**How many 6-digit numbers are there in all?**

**Solution:**

The largest 6-digit number = 999999

The smallest 6-digit number = 100000

Therefore, Total number of 6-digit numbers = (999999 – 100000) + 1

= 899999 + 1

= 900000

= 9 lakhs

**Question 8:**

**How many 7-digit numbers are there in all?**

**Solution:**

The largest 7-digit number = 9999999

The smallest 7-digit number = 1000000

Therefore, Total number of 7-digit numbers = (9999999 – 1000000)

= 8999999 + 1

= 9000000

= Ninety lakhs

**Question 9:**

**How many thousands make a lakh?**

**Solution:**

One lakh (1,00,000) is equal to one hundred thousand (100 x 1000).

Thus, one hundred thousand make a lakh.

**Question 10:**

**How many thousands make a crore?**

**Solution:**

One crore (1,00,00,000) is equal to one hundred lakh (10,000 x 1,000).

Thus, 10,000 thousands make a crore.

**Question 11:**

**Find the difference between the number 738 and that obtained on reversing its digits.**

**Solution:**

The given number is 738.

On reversing the digits of this number, we get 837.

Therefore, Required difference = 837 – 738 = 99

**Question 12:**

**What comes just after 9547999?**

**Solution:**

The number just after 9547999 is 9547999 + 1 = 9548000.

**Question 13:**

**What comes just before 9900000?**

**Solution:**

The number just before 9900000 is 9900000 – 1 = 9899999.

**Question 14:**

**What comes just before 10000000?**

**Solution:**

The number just before 10000000 is 10000000 – 1 = 9999999.

**Question 15:**

**Write all 3-digit numbers using 2, 3, 4, taking each digit only once.**

**Solution:**

The 3-digit numbers formed by 2, 3 and 4 by taking each digit only once are 234, 324, 243, 342, 423 and 432.

**Question 16:**

**Write the smallest number of different digits formed by using the digits 3, 1, 0, 5 and 7.**

**Solution: **

The smallest number formed by using each of the given digits (i.e., 3, 1, 0, 5 and 7) only once is 10357.

**Question 17:**

**Write the largest number of different digits formed by using the digits 2, 4, 0, 3, 6 and 9.**

**Solution:**

The largest number formed by using each of the given digits only once is 964320.

**Question 18:**

**Rewrite each of the following numerals with proper commas, using the international place-value chart. Also, write the number name of each in the international system.**

**(i) 735821**

**(ii) 6057894**

**(iii) 56943821**

**(iv) 37502093**

**(v) 89350064**

**(vi) 90703006**

**Solution:**

Representation of the numbers on the international place-value chart:

Periods |
Millions |
Thousands |
Ones |
||||||

Place | Hundred millions | Ten millions | Millions | Hundred thousands | Ten thousands | Thousands | Hundreds | Tens | Ones |

HM | TM | M | H Th | T Th | Th | H | T | O | |

(i) | 7 | 3 | 5 | 8 | 2 | 1 | |||

(ii) | 6 | 0 | 5 | 7 | 8 | 9 | 4 | ||

(iii) | 5 | 6 | 9 | 4 | 3 | 8 | 2 | 1 | |

(iv) | 3 | 7 | 5 | 0 | 2 | 0 | 9 | 3 | |

(v) | 8 | 9 | 3 | 5 | 0 | 0 | 6 | 4 | |

(vi) | 9 | 0 | 7 | 0 | 3 | 0 | 0 | 6 | |

Crore | Ten lakhs | Lakhs | Ten Thousand | Thousand | Hundred | Tens | Ones |

The number names of the given numbers in the international system:

(i) 735,821 = Seven hundred thirty-five thousand eight hundred twenty-one

(ii) 6,057,894 = Six million fifty-seven thousand eight hundred ninety-four

(iii) 56,943,821 = Fifty-six million nine hundred forty-three thousand eight hundred twenty-one

(iv) 37,502,093 = Thirty-seven million five hundred two thousand ninety-three

(v) 89,350,064 = Eighty-nine million three hundred fifty thousand sixty-four

(vi) 90,703,006 = Ninety million seven hundred three thousand and six

**Question 19:**

**Write each of the following in figures in the international place-value chart:**

**(i) Thirty million one hundred five thousand sixty-three**

**(ii) Fifty-two million two hundred five thousand six**

**(iii) Five million five thousand five**

**Solution:**

Periods |
Millions |
Thousands |
Ones |
||||||

Place | Hundred millions | Ten millions | Millions | Hundred thousands | Ten thousands | Thousands | Hundreds | Tens | Ones |

HM | TM | M | H Th | T Th | Th | H | T | O | |

(i) | 3 | 0 | 1 | 0 | 5 | 0 | 6 | 3 | |

(ii) | 5 | 2 | 2 | 0 | 5 | 0 | 0 | 6 | |

(iii) | 5 | 0 | 0 | 5 | 0 | 0 | 5 |

**Exercise 1B**

**Fill in each of the following boxes with the correct symbol > or < :**

**Question 1:**

**1003467 ___987965**

**Solution:**

1003467 > 987965

We know that a 7-digit number is always greater than a 6-digit number. Since 1003467 is a 7-digit number and 987965 is a 6-digit number, 1003467 is greater than 987965.

**Question 2:**

**3572014 ___10235401**

**Solution:**

3572014 < 10235401

We know that a 7-digit number is always less than an 8-digit number. Since 3572014 is a 7-digit number and 10235401 is an 8-digit number, 3572014 is less than 10235401.

**Question 3:**

**3254790 ___3260152**

**Solution:**

Both the numbers have the digit 3 at the ten lakhs places.

Also, both the numbers have the digit 2 at the lakhs places.

However, the digits at the ten thousands place in 3254790 and 3260152 are 5 and 6, respectively.

Clearly, 5 < 6

Therefore, 3254790 < 3260152

**Question 4:**

**10357690 ___11243567**

**Solution:**

Both have the digit 1 at the crores places.

However, the digits at the ten lakhs places in 10357690 and 11243567 are 0 and 1, respectively.

Clearly, 0 < 1

Therefore, 10357690 < 11243567

**Question 5:**

**27596381 ___7965412**

**Solution:**

27596381 > 7965412

We know that an 8-digit number is always greater than a 7-digit number. Since 7965412 is a 7-digit number and 27596381 is 8-digit number, 27596381 is greater than 7965412.

**Question 6:**

**47893501 ___47894021**

**Solution:**

Both the numbers have the same digits, namely 4, 7, 8 and 9, at the crores, ten lakhs, lakhs and ten thousands places, repectively.

However, the digits at the thousands place in 47893501 and 47894021 are 3 and 4, respectively.

Clearly, 3 < 4

Therefore, 47893501 < 47894021

**Arrange the following numbers in descending order:**

**Question 7:**

**63521047, 7354206, 63514759, 7355014, 102345680**

**Solution:**

102345680 is a 9-digit number.

63521047 and 63514759 are both 8-digit numbers.

Both the numbers have the same digits, namely 6, 3 and 5, at the crores, ten lakhs and lakhs places, respectively.

However, the digits at the ten thousands place in 63521047 and 63514759 are 2 and 1, respectively.

Clearly 2 > 1

Therefore, 63521047 > 63514759

7355014 and 7354206 are both 7-digit numbers.

Both the numbers have the same digits, namely 7, 3 and 5 at the crores, ten lakhs and lakhs places, respectively.

However, the digits at the ten thousands place in 7355014 and 7354206 are 5 and 4, respectively.

Clearly, 5 > 4

Therefore, 7355014 > 7354206

The given numbers in descending order are:

1023456080 > 63521047 > 63514759 > 7355014 > 7354206

**Question 8:**

**5032786, 23794206, 5032790, 23756819, 987876**

**Solution:**

23794206 and 23756819 are both 8-digit numbers.

Both the numbers have the same digits, namely 2, 3 and 7 at the crores, ten lakhs and lakhs places, respectively.

However, the digits at the ten thousands place in 23794206 and 23756819 are 9 and 5, respectively.

Clearly, 9 > 5

Therefore, 23794206 > 23756819

5032790 and 5032786 are both 7-digit numbers.

Both the numbers have the same digits, namely 5, 0, 3, 2 and 7, at the ten lakhs, lakhs, ten thousands, thousands and hundreds place, respectively.

However, the digits at the tens place 5032790 and 5032786 are 9 and 8, respectively.

Clearly, 9 > 8

Therefore, 5032790 > 5032786

987876 is a 6-digit number.

The given numbers in descending order are:

23794206 > 23756819 > 5032790 > 5032786 > 987876

**Question 9:**

**19090, 1808088, 16060666, 16007777, 181888, 1808090**

**Solution:**

16060666 and 16007777 are both 8-digit numbers.

Both the numbers have the same digits, namely 1, 6 and 0, at the crores, ten lakhs and lakhs places, respectively.

However, the digits at the ten thousands place is 16060666 and 16007777 are 6 and 0, respectively.

Clearly, 6 > 0

Therefore, 16060666 > 16007777

1808090 and 1808088 are both 7-digit numbers.

Both the numbers have the same digits, namely 1, 8, 0, 8 and 0, at ten lakhs, ten thousands, thousands and hundred places, respectively.

However, the digits at the tens place in 1808090 and 1808088 are 9 and 8, respectively.

Clearly, 9 > 8

Therefore, 1808090 > 1808088

190909 and 181888 are both 6-digit numbers.

Both the numbers have the same digit, 1, at the lakhs place.

However, the digits at the ten thousands place in 190909 and 181888 are 9 and 8, respectively.

Clearly, 9 > 8

Therefore, 190909 > 181888

Thus, the given numbers in descending order are:

16060666 > 16007777 > 1808090 > 1808088 > 190909 > 181888

**Question 10:**

**199988, 1704382, 200175, 1702497, 201200, 1712040**

**Solution:**

1712040, 1704382 and 1702497 are all 7-digit numbers.

The three numbers have the same digits, namely 1 and 7, at ten lakhs and lakhs places, respectively.

However, the digits at the ten thousands place in 1712040, 1704382 and 1702497 are 1, 0 and 0.

Therefore, 1712040 is the largest.

Of the other two numbers, the respective digits at the thousands places are 4 and 2.

Clearly, 4 > 2

Therefore, 1704382 > 1702497

201200, 200175 and 199988 are all 6-digit numbers.

At the lakhs place, we have 2 > 1.

So, 199988 is the smallest of the three numbers.

The other two numbers have the same digits, namely 2 and 0, at the lakhs and ten thousands places, respectively.

However, the digits at the thousands place in 201200 and 200175 are 1 and 0, respectively.

Clearly, 1 > 0

Therefore, 201200 > 200175

The given numbers in descending order are:

1712040 > 1704382 > 1702497 > 201200 > 200175 > 199988

**Arrange the following numbers in ascending order:**

**Question 11:**

**9873426, 24615019, 990357, 9874012, 24620010**

**Solution:**

990357 is a 6-digit number.

9873426 and 9874012 are both 7-digit numbers.

Both the numbers have the same digits, namely 9, 8 and 7, at the ten lakhs, lakhs and ten thousands places, respectively.

However, the digits at the thousands place in 9873426 and 9874012 are 3 and 4, respectively.

Clearly, 4 < 7

Therefore, 9873426 < 9874012

24615019 and 24620010 are both 8-digit numbers.

Both the numbers have the same digits, namely 2, 4 and 6, at the crores, ten lakhs and lakhs places, respectively.

However, the digits at the ten thousands place in 24615019 and 24620010 are 2 and 1, respectively.

Clearly, 1 < 2

Therefore, 24615019 < 24620010

The given numbers in ascending order are:

990357 < 9873426 < 9874012 < 24615019 < 24620010

**Question 12:**

**56943201, 5694437, 56944000, 5695440, 56943300**

**Solution:**

5694437 and 5695440 are both 7-digit numbers.

Both have the same digit, i.e., 5 at the ten lakhs place.

Both have the same digit, i.e., 6 at the lakhs place.

Both have the same digit, i.e., 9 at the ten thousands place.

However, the digits at the thousand place in 5694437 and 5695440 are 4 and 5, respectively.

Clearly, 4 < 5

Therefore, 5694437 < 5695440

56943201, 56943300 and 56944000 are all 8-digit numbers.

They have the same digit, i.e., 5 at the crores place.

They have the same digit, i.e., 6 at the ten lakhs place.

They have the same digit, i.e., 9 at the lakhs place.

They have the same digit, i.e., 5 at the ten thousands place.

However, at the thousands place, one number has 4 while the others have 3.

Therefore, 56944000 is the largest.

The other two numbers have 3 and 2 at their hundreds places.

Clearly, 2 < 3

Therefore, 56943201 < 56943300

The given numbers in ascending order are:

5694437 < 5695440 < 56943201 < 56943300 < 56944000

**Question 13:**

**700087,8014257, 8015032, 10012458, 8014306**

**Solution:**

700087 is 6-digit number.

8014257, 8014306 and 8015032 are all 7-digit numbers.

They have the same digits, namely 8, 0 and 1, at the ten lakhs, lakhs and ten thousands places, respectively.

But, at the thousands place, one number has 5 while the other two numbers have 4.

Here, 801503 is the largest.

The other two numbers have 2 and 3 at their hundreds places.

Clearly, 2 < 3

Therefore, 8014306 < 8015032

10012458 is an 8-digit number.

The given numbers in ascending order are:

700087 < 8014257 < 8014306 < 8015032 < 10012458

**Question 14:**

**1020304, 893245, 980134, 1021403, 893425, 1020216**

**Solution:**

893245, 893425 and 980134 are all 6-digit numbers.

Among the three, 980134 is the largest.

The other two numbers have the same digits, namely 8, 9 and 3, at the lakhs, ten thousands and thousands places, respectively.

However, the digits at the hundreds place in 893245 and 893425 ae 2 and 4, respectively.

Clearly, 2 < 4

Therefore, 893245 < 893425

1020216, 1020304 and 1021403 are all 7-digit numbers.

They have the same digits, namely 1, 0 and 2, at the ten lakhs, lakhs and ten thousands places, respectively.

At the thousands place, 1021403 has 1.

The other two numbers have the digits 2 and 3 at their hundred places.

Clearly, 2 < 3

Therefore, 1020216 < 1020304

The given numbers in ascending order are:

893245 < 893425 < 980134 < 1020216 < 1020304 < 1021403

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