RATIONAL IRRATIONAL AND DECIMAL WORKSHEET

Question 1 :

On the number line below, the marks are equally spaced. What is the coordinate of P?

Question 2 :

Round 52.348 to the nearest

a) integer and b) hundredth.

Question 3 :

On the number line above, if BC = 2AB, then find the value of 'x'.

Question 4 :

Which of the following is an irrational number?

A) -1.2

B) 4/3

C) -√16

D) -√10

Question 5 :

Which of the following is a rational number?

A) √1.6

B) -√250

C) √0.9

D) √(49/64)

Question 6 :

Find the number which is halfway between -5/6 and 1/3 on a number line.

Answers

1. Answer :

Since the distance between the marks is 0.25, the coordinate of P is

= 70.25 x (-1.75)

= -1.75

2. Answer :

Part (a) :

Underline 2, the digit in the ones place. 52.348

The digit to the right of the underlined digit is less than 5, keep the underlined digit as it is.

Therefore, 52.348 rounded to the nearest integer is 52.

Part (b) :

Underline 4, the digit in the hundredths place. 52.348

The digit to the right of the underlined digit is more than 5, round up.

Therefore, 52.348 rounded to the nearest hundredths place is 52.35.

3. Answer :

BC = 2AB

C - B = 2(B - A)

x - (-0.4) = 2[-0.4 - (-1.25)]

x + 0.4 = 2(-0.4 + 1.25)

x + 0.4 = 2(0.85)

x + 0.4 = 1.7

Subtract 0.4 from both sides.

x = 1.3

4. Answer :

A) -1.2 :

-1.2 = -12/10

= -6/5

-6/5 is in the form of a/b

-1.2 is a rational number.

B) 4/3 :

4/3

4/3 is in the form of a/b

4/3 is a rational number.

C) -√16 :

-√16 = -4

= -4/1

-4/1 is in the form of a/b

-√16 is a rational number.

D) -√10 :

-√10 = -3.16227.........

-3.16227 is a non terminating and non repeating decimal.

-√10 is an irrational number.

The correct answer choice is (D) -√10.

5. Answer :

A) √1.6 :

16 is a perfect square. But 1.6 is not a perfect square.

4² = 16, but

(0.4)² = 0.4 x 0.4 = 0.16 

(0.4)² ≠ 1.6

Since the number 1.6 inside the square root is not a perfect square, √1.6 is an irrational number.

B) -√250 :

We know that 225 (= 15²) is a perfect square  and the next perfect square is 289 (= 17²). Any number between 225 and 289 can not be a perfect square. So, 250 is not a perfect square.  

Since the number 250 inside the square root is not a perfect square, √250 is an irrational number.

C) √0.9 :

9 is a perfect square. But 0.9 is not a perfect square.

3² = 9, but

(0.3)² = 0.3 x 0.3 = 0.09 

(0.3)² ≠ 0.9

Since the number 0.9 inside the square root is not a perfect square, √0.9 is an irrational number.

D) √(49/64) :

√(49/64) = √49/√64

= 7/8

7/8 is in the form of a/b

√(49/64) is a rational number.

The correct answer choice is (D) √(49/64).

6. Answer :

To find a number on a number line which is halfway between two numbers, find the average of the two numbers.

Average of -5/6 and 1/3 = (-5/6 + 1/3) ÷ 2

= (-5/6 + 2/6) ÷ 2

= (-5 + 2)/6 ÷ 2

 = -3/6 ÷ 2

= -1/2 ÷ 2

= -1/2 x 1/2

= -1/4

On a number line, -1/4 is a number between -5/6 and 1/3.

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