from a handpicked tutor in LIVE 1-to-1 classes

# Express the following in the form p/q, where p and q are integers and q ≠ 0.

i) 0.6 ii) 0.47 iii) 0.001

**Solution:**

i) 0.6

Let x = 0.6

x = 0.666 ........(1)

Since one digit is repeating after the decimal, we will multiply both sides of equation (1) by 10.

This gives us,

10x = 6.666...

10x = 6 + 0.666

10x = 6 + x [From equation (1)]

10x - x = 6

9x = 6

x = 6/9

x = 2/3

Thus, 0.6 = 2/3

ii) 0.47

Let x = 0.4777 ........(1)

Here, the repetition starts after the first decimal place and one digit is repeated. Thus, we multiply both sides of equation (1) by 10.

10x = 4.777 ........(2)

We will subtract equation (1) from equation (2).

10x - x = 4.777... - 0.4777...

9x = 4.3

9x = 43/10

x = 43/90

Thus, 0.47 = 43/90

iii) 0.001

Let x = 0.001001 ......(1)

Since 3 digits are repeated, multiply both the sides of equation (1) by 1000.

1000x = 1.001001

1000x = 1 + 0.001001

1000x = 1 + x [From equation (1)]

1000x - x = 1

999x = 1

x = 1/999

Thus, 0.001 = 1/999

**☛ Check: **NCERT Solutions Class 9 Maths Chapter 1

**Video Solution:**

## Express the following in the form of p/q, where p and q are integers and q ≠ 0. i) 0.6 ii) 0.47 iii) 0.001

NCERT Solutions Class 9 Maths Chapter 1 Exercise 1.3 Question 3:

**Summary:**

Thus, 0.6, 0.47, 0.001 can be expressed in the form of p/q as 2/3, 43/90, and 1/999 respectively

**☛ Related Questions:**

- Write the following in decimal form and say what kind of decimal expansion each has: i) 36/100 ii) 1/11 iii) 4 1/8 iv) 3/13 v) 2/11 vi) 329/400
- You know that 1/7 = 0.142587. Can you predict what the decimal expansions of 2/7, 3/7, 4/7, 5/7, 6/7 are, without actually doing the long division? If so, how?
- Express 0.99999 .... in the form of p/q. Are you surprised with your answer? With your teacher and classmates discuss why the answer makes sense?
- What can be the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17? Perform the division to check your answer.

visual curriculum