## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 1 Knowing Our Numbers Objective Type Questions

**Mental Maths
**Question 1.

Fill in the blanks:

(i) The digit …………… has the highest place value in the number 2309.

(ii) The digit …………… has the highest face value in the number 2039.

(iii) The digit …………… has the lowest place value in the number 2039.

(iv) Both Indian and International systems of numeration have …………… period in common.

(v) In the International system of numeration, commas are placed from …………… after every …………… digits.

(vi) The bigger number from the numbers 57,631 and 57,361 is ……………

(vii) 1 crore = …………… million

(viii)The smallest 4-digit number with 3 different digits is ……………

(ix) The greatest 4-digit number with 3 different digits is ……………

(x) 15 km 300 m = …………… m

(xi) 7850 cm = …………… m …………… cm

(xii) The number 5079 when estimated to the nearest hundreds is ……………

Solution:

(i) The digit 2 has the highest place value in the number 2309.

(ii) The digit 9 has the highest face value in the number 2039.

(iii) The digit 0 has the lowest place value in the number 2039.

(iv) Both Indian and International systems of numeration have ones period in common.

(v) In the International system of numeration, commas are placed from right after every 3 digits.

(vi) The bigger number from the numbers 57,631 and 57,361 is 57,631.

(vii) 1 crore = 10 million (viii)The smallest 4-digit number with 3 different digits is 1002.

(ix) The greatest 4-digit number with 3 different digits is 9987.

(x) 15 km 300 m = 15300 m

(xi) 7850 cm = 78 m 50 cm

(xii) The number 5079 when estimated to the nearest hundreds is 5100.

Question 2.

State whether the following statements are true (T) or false (F):

(i) The difference between the place value and the face of the digit 7 in the number 2701 is 693.

(ii) The smallest 4-digit number -1 = the greatest 3-digit number.

(iii) The place of a digit is independent of whether the number is written in the Indian system or International system of numeration.

(iv) In the International system, a number having less number of digits is always smaller than the number having more number of digits.

(v) The estimated value of 9999 to the nearest tens is 10000.

Solution:

(i) The difference between the place value and the face of the digit 7 in the number 2701 is 693. True

(ii) The smallest 4-digit number-1 = the greatest 3-digit number. True

(iii) The place of a digit is independent of whether the number is written in the Indian system or International system of numeration.

True

(iv) In the International system, a number having less number of digits is always smaller than the number having more number of digits.

True

(v) The estimated value of 9999 to the nearest

**Multiple Choice Questions**

**Choose the correct answer from the given four options (3 to 17):**

Question 3.

The face value of the digit 5 in the number 36503 is

(a) 5

(b) 503

(c) 500

(d) none of these

Solution:

The place value of 5 at hundred’s place

= 5 × 100 = 500 (c)

Question 4.

The difference between the place values of 6 and 3 in 76834 is

(a) 3

(b) 5700

(c) 5930

(d) 5970

Solution:

The place value of 6 at thousand’s place

= 6 × 1000 = 6,000

The place value of 3 at ten’s place

= 3 × 10 = 30

The difference between the place value of 6 and 3 = 6000 – 30 = 5970 (d)

Question 5.

The sum of the place values of all the digits in 5003 is

(a) 8

(b) 53

(c) 5003

(d) 8000

Solution:

The place value of 3 at one’s place

=3 × 1 = 3

The place value of 0 at ten’s place = 0 × 10 = 0

The place value of 0 at hundred’s place = 0 × 100 = 0

The place value of 5 at thousand’s place = 5 × 1000 = 5000

The sum of the place value of all the digits

in 5003 = 3 + 0 + 0 + 5000 = 5003 (c)

Question 6.

The total number of 4-digit numbers is

(a) 9000

(b) 9999

(c) 10000

(d) none of these

Solution:

The greatest 3-digit number = 999 The greatest 4-digit number = 9999 .’. The total number of 4-digit numbers

= 9999 – 999 = 9000 (a)

Question 7.

The product of the place values of two-threes in 73532 is

(a) 9000

(b) 90000

(c) 99000

(d) 1000

Solution:

The place value of 3 at ten’s place = 3 × 10 = 30

The place value of 3 at thousand’s place = 3 × 1000 = 3000

The product of place value of two threes = 30 × 3000 = 90000 (b)

Question 8.

The smallest 4-digit number having distinct digits is

(a) 1234

(b) 1023

(c) 1002

(d) 3210

Solution:

The smallest 4-digit number having distinct digits is 1002. (c)

Question 9.

The largest 4-digit number having distinct digits is

(a) 9999

(b) 9867

(c) 9786

(d) 9876

Solution:

The largest 4-digit number having distinct digits is 9867. (b)

Question 10.

The largest 4-digit number is

(a) 9999

(b) 9876

(c) 9990

(d) none of these

Solution:

The largest 4-digit number is 9999. (a)

Question 11.

The difference between the largest number of 3-digit and the largest number of 3-digit with distinct digits is

(a) 0

(b) 10

(c) 12

(d) 14

Solution:

The largest number of 3-digit = 999

The largest number of 3-digit with distinct digits = 987

∴ Their difference = 999 – 987 = 12 (c)

Question 12.

If we write natural numbers from 1 to 100, the number of times the digit 5 has been written is

(a) 11

(b) 15

(c) 19

(d) 20

Solution:

If we write natural numbers from 1 to 100, the number of times the digit 5 has been written is 20. (d)

Question 13.

The number 28,549 when rounded off to the nearest hundreds is

(a) 28,000

(b) 28,500

(c) 28,600

(d) 29,000

Solution:

28,549

The digit at tens place is 4, which is less than 5.

Hence, the rounded off number to nearest hundreds = 28,500. (b)

Question 14.

The smallest natural number which when rounded off to the nearest hundreds as 500 is

(a) 499

(b) 501

(c) 450

(d) 549

Solution:

The smallest natural number which when rounded off to the nearest hundreds as 500 is 450. (c)

This is so because the digit at tens place is 5, which is equal to 5.

Question 15.

The greatest natural number which when rounded off to the nearest hundreds as 500 is

(a) 549

(b) 599

(c) 450

(d) none of these

Solution:

The greatest natural number which when rounded off to the nearest hundreds as 500 is 549. (a)

This is so because the digit at tens place is 4, which is less than 5.

Question 16.

The greatest 5-digit number formed by the digits 3, 0, 7 is

(a) 33077

(b) 77730

(c) 77330

(d) none of these

Solution:

The greatest 5-digit number formed by the digits 3, 0, 7 is 77730. (b)

Question 17.

In the International place value system, we write 1 billion for

(a) 10 lakh

(b) 1 crore

(c) 10 crore

(d) 100 crore

Solution:

In the International place value system, we write 1 billion for 100 crore. (d)

**Value Based Questions**

Question 1.

The distance between Anu’s home and her school is 4 km 850 m. Everyday she cycles both ways. Find the distance covered by her in a week. (Sunday being a holiday).

What are the advantages of cycling?

Solution:

Distance between Anu’s home and her school = 4 km 850 m = 4 x 1000+ 850 = 4850 m Distance travelled by Anu per day = 4850 m x 2 = 9700 m Since, in a week there are 7 days but Sunday is off.

Hence, distance travelled by Anu for 6 days (a week) = 9700 × 6 = 58200 m

= 58 km 200 m

Cycling is good for health and it saves fuel and helps in reducing pollution.

**Higher Order Thinking Skills (HOTS)**

Question 1.

Is there any digit whose place value is always equal to its face value irrespective of its position in any number?

Solution:

Yes, the digit is 0.

Question 2.

Write all 4-digit numbers that can be formed with the digits2 and 5, using both digits equal number of time. Also find their sum.

Solution:

Possible numbers are : 2255, 2552, 2525, 5225, 5252, 5522

and their sum = 2255 + 2552 + 2525 + 5225 + 5252 + 5522 = 23331

Thousand |
Hundred |
Tens |
Ones |

2 | 2 | 5 | 5 |

2 | 5 | 5 | 2 |

2 | 5 | 2 | 5 |

5 | 2 | 2 | 5 |

5 | 2 | 5 | 2 |

5 | 5 | 2 | 2 |

Question 3.

What is the difference between the smallest 6-digit number with five different digits and the greatest 5-digit number with four different digits?

Solution:

The smallest 6-digit number with five different digits = 100234.

The greatest 5-digit number with four different digits = 99876.

Their difference = 100234 – 99876 = 358

Question 4.

How many times does the digit 3 occur at tert’s place in natural numbers from 100 to 1000?

Solution:

90 times i.e. 3, 13, 23, 33, 43, 53, 63, 73, 83, 93 and upto 983, 993