Question

Express (i) 1.4191919.... (ii) 0.001 in the form p/q, where p and q are integers and q neq 0.

a) 281/198 , 1/999
b) 198/281 , 999/1
c) 1/198 , 999/1000
d) 198/1 , 1000/999

Answer 1

To express the repeating decimal 1.4191919... as a fraction, we can use the method of converting the repeating decimal to a fraction. The answer is a) 281/198. The number 0.001 can be expressed as the fraction 198/1.

Step-by-step explanation:

To express a repeating decimal in the form p/q, where p and q are integers and q ≠ 0, we can use the method of converting the repeating decimal to a fraction. Let's start by considering the number 1.4191919...

We can represent this as an equation:

x = 1.4191919...

Multiplying both sides of the equation by 100 gives:

100x = 141.9191919...

Subtracting the original equation from the multiplied equation eliminates the repeating part:

99x = 141.9191919... - 1.4191919...

Calculating the right side of the equation gives:

99x = 140.5

Dividing both sides of the equation by 99 gives:

x = 140.5/99

Simplifying the fraction gives:

x = 281/198

Therefore, the answer to (i) is a) 281/198.

To express the number 0.001 in the form p/q, we can write it as 1/1000.

Therefore, the answer to (ii) is d) 198/1.