Question

express the following in the form p/q, where p and q are Integers and q≠0.

1. 6.33333...

2. 0.001001001...

3. 0.6666...

4. 0.99999..

Answer 1

hiii!!!

here's ur answer...

1. let x = 6.3333... --------(1)

multiplying both sides by 10 as one number is repeating.

10 × x = 10 × 6.333...

10x = 63.333... --------(2)

subtract equation (1) from equation (2)

10x - x = 63.333... - 6.333...

9x = 57

x = 57/9

2. let x = 0.001001001... --------(1)

multiplying both sides by 1000 as 3 numbers are repeating.

1000 × x = 1000 × 0.001001001...

1000x = 1.001001001... --------(2)

subtract equation (1) from equation (2)

1000x - x = 1.001001001... - 0.001001001...

999x = 1

x = 1/999

3. let x = 0.666... --------(1)

multiplying both sides by 10 as one number is repeating.

10 × x = 10 × 0.666...

10x = 6.666... --------(2)

subtract equation (1) from equation (2)

10x - x = 6.666... - 0.666...

9x = 6

x = 6/9

x = 2/3

4. let x = 0.999... --------(1)

multiplying both sides by 10 as one number is repeating.

10 × x = 10 × 0.999...

10x = 9.999... --------(2)

subtract equation (1) from equation (2)

10x - x = 9.999... - 0.999...

9x = 9

x = 9/9

x = 1/1

hope this helps u..!!