CBSE Class 9 Mathematics Number System Worksheet Set A

1. Round each the following numbers to the nearest ten
a. 36
b. 3869
Answer.
a. 36
In, 36 is one digit 6>5 So required rounded number =40
Answer 40

b. 3869
In 173, the one digit is 9<5
So, the required rounded number = 3870
Answer 3870

2. Round each of the following numbers to nearest thousand
a. 793
b. 4826
Answer.
a. 793
In 793 the hundred digit is 7>5
So, the required rounded number1 000
Answer 1000

b. 4826 In 4826 the hundred digit is 8>5
So, the required rounded number 5000
Answer 5000

3. Estimate each sum to the nearest hundred.
a. (236+689)
b. (170+395)
Answer.
a. (236+689)
236 estimated to nearest hundred =200
689 estimated to nearest hundred is =700
So, the require estimation = (200+700)= 900
Answer 900

b. (170+395) 170 estimated to nearest hundred = 200
395 estimated to nearest hundred = 400
the require estimation = (200+400)= 600
Answer 600

4. Estimate each difference to the nearest ten.
a. (54-18)
b. (97-38)
Answer.
a. (54-18)
54 estimated to the nearest ten = 50
18 estimated to nearest ten = 20
So, the require estimation = (50-20) = 30

b. (97-38) 97 estimated to the nearest ten = 100
38 estimated to nearest ten = 40
So, the require estimation = (100-40)= 60

5. Estimate each the following product by rounding of each number to nearest ten.
a. 38×63
b. 15×34
Answer.
a. 38×63
38 estimated to the nearest ten = 40
63 estimated to nearest ten = 60
So, the require estimation = (40×60)= 2400

b. 15×34 15 estimated to the nearest ten = 20
34 estimated to nearest ten = 30
So, the require estimation = (20×30)= 600

6. Find the estimate quotient for each of the following
a. 87÷ 28
b. 275÷25
Answer.
a. 87÷ 28
87÷ 28 is approx equal to 90÷30 = 3

b. 275÷25
The estimated quotient of 275÷25 is approx equal to 300÷30 = 30÷3 = 10

7. Express each of the following as a roman numeral.
a. 43
b. 61
c. 99
d. 114
Answer.
a. 43
43 = (50-10)+3 = XLIII
Answer XLIII

b. 61
61 = 50+10+1 = LXI
Answer LXI

c. 99
99 = (100-1)+9 = XCIX
Answer XCIX

d. 114 114 = (100+10)+4 = CXIV
Answer CXIV

8. Write each of the following as a Hindu Arabic numeral.
a. XXVII
b. CCXXIV
c. DVI
d. CDLXIV
Answer.
a. XXVII = 10+10+7 = 27
Answer 27

b. CCXXIV = 100+100+10+10+4 = 224
Answer 224

c. DVI = 500+6 = 506
Answer 506

d. CDLXIV = (500-100)+ 50+10+4 = 464
Answer 464

9. Word problem.
a. The coast of a steel almirah is Rs. 22875. What is the coast of 465 such almirahs?
b. For making 16 shirt, 44 meters of cloth is needed. How much cloth is required for each shirt?
Answer.
a. The coast of a steel almirah is Rs. 22875. What is the coast of 465 such almirahs?
Solution – Cost of 1 almirah = Rs 22875
Cost of 465 almirahs = Rs. ( 22875×465)
                              = 10636875
Hence, the cost of 465 almirahs is Rs. 10636875

b. For making 16 shirt, 44 meters of cloth is needed. How much cloth is required for each shirt?
Cloth required for 16 shirts = 44 m
Cloth required for each shirt = (44m) ÷16
                                         = 2 m 75 cm
Hence, the cloth required for each shirt = 2 m 75 cm

ASSERTION REASONING QUESTIONS

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R).
Mark the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion : Rational number lying between two rational numbers x and y is 1/2(x + y) .
Reason : There is one rational number lying between any two rational numbers.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that there are infinitely many rational numbers between any two given rational numbers.
So, Reason is not correct.
One of the rational number lying between two rational numbers x and y is 1/2(x + y) .
So, Assertion is correct
Correct option is (c) Assertion (A) is true but reason (R) is false.

Question. Assertion : 5 is a rational number.
Reason : The square roots of all positive integers are irrationals.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : Here reason is not true.
√4 = ±2, which is not an irrational number.
Correct option is (c) Assertion (A) is true but reason (R) is false.

Question. Assertion : Sum of two irrational numbers 2 + √3 and 4 + √3 is irrational number.
Reason : Sum of two irrational numbers is always an irrational number.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : Here, 2 + √3 + 4 + √3 = 6 + 2√3 which is an irrational number.
So, Assertion is correct.
Now, 2 + √3 and 4 – √3 are two irrational numbers
Sum = 2 + √3 + 4 – √3 = 6 which is a rational number.
So, Reason is not correct.
Correct option is (c) Assertion (A) is true but reason (R) is false

Question. Assertion : Sum of two irrational numbers 2 + √3 is an irrational number.
Reason : Sum of a rational number and an irrational numbers is always an irrational number.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that the sum of a rational number and an irrational numbers is always an irrational number.
So, Reason is correct.
Now, 2 + √3 is an irrational numbers
So, Assertion is also correct.
Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .

Question. Assertion : 11³ x 11⁴ = 11¹²
Reason : If a > 0 be a real number and p and q be rational numbers.
Then a^p x a^q = a^p + q.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that If a > 0 be a real number and p and q be rational numbers then a^p x a^q = a^p+q.
So, Reason is true.
Now, 11³ x 11⁴ = 11³⁺⁴ = 11⁷
Here assertion is incorrect but reason is correct.
Correct option is (d) Assertion (A) is false but reason (R) is true

Question. Assertion : 7⁸ ÷ 7⁴ = 7⁴
Reason : If a > 0 be a real number and p and q be rational numbers.
Then a^p x a^q = a^{p + q}
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that If a > 0 be a real number and p and q be rational numbers then ap x aq = ap+q.
So, Reason is correct.
Now, 7⁸ ÷ 7⁴ = 7^{8 – 4} = 7⁴         (∴ a^p ÷ a^q = a^{p – q})
So, Assertion is also correct.
But reason (R) is not the correct explanation of assertion (A)
Correct option is (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .

Question. Assertion : Rational number lying between 1/4 and 1/2 is 3/8
Reason : Rational number lying between two rational numbers x and y is 1/2(x y) .
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that Rational number lying between two rational numbers x and y is 1/2(x + y) .
So, Reason is not correct.
Now, 1/2(1/4+1/2) = 1/2 (1+2/4) = 3/8
So, Assertion is correct
Correct option is (c) Assertion (A) is true but reason (R) is false.

Question. Assertion : √5 is an irrational number.
Reason : A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that “A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q ≠ 0.”
So, Reason is correct.
Since, √5 cannot be written in the form of p/q, therefore it is an irrational number.
Hence assertion is correct follows from reason.
Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .

Question. Assertion : 0.329 is a terminating decimal.
Reason : A decimal in which a digit or a set of digits is repeated periodically, is called a repeating, or a recurring, decimal.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that a decimal in which a digit or a set of digits is repeated periodically, is called a repeating, or a recurring, decimal.
So, Reason is correct.
Also, we know that a decimal that ends after a finite number of digits is called a terminating decimal.
Hence Assertion is correct but reason is not the correct explanation of Assertion
Correct option is (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .

Question. Assertion : The rationalizing factor of 3 + 2√5 is 3 – 2√5.
Reason : If the product of two irrational numbers is rational then each one is called the rationalising factor of the other.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that If the product of two irrational numbers is rational then each one is called the rationalising factor of the other.
So, Reason is correct.
Now, (3 + 2√5) x (3 – 2√5) = 32 – (2√5) ²
= 9 – 20 = – 11
So, both Assertion and Reason are correct and Reason explains Assertion.
Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .