Question

express 15.712 with bar on 12 in p/q form

Answer 1

Let x be 15.712(bar on 12)

As the number of reccuring(repeating) decimals is 2,we will have to multiply the x=15.712(bar on 12) with 100.

We will get:

100x=1571.212(bar on 12).

Now we are supposed to subtract x from 100x and we should even subtract their values.

We will get:

100x-x=1571.212(bar on 12)-15.712(bar on 12).

99x=1501.5

x=1501.5/99

So now we have found the p/q form of 15.712(bar on 12) but still p is not an integer where as q is an integer which is not equal to 0.

So we should multiply 1501.5/99*10/10 to make it in the form of p/q where p and q are integers and q is not equal to 0.

So 15.712(bar on 12) in the form of p/q where p and q are integers and q is not equal to 0 is 15015/990.

This can further be simplified to 5005/330 = 1001/66.

Therefore the final answer is 15.712(bar on 12) = 1001/66.

Answer 2

Concept: Real numbers are two types: Rational and irrational.

Rational numbers are those numbers, which are in the form of p/q where p≠0.

Find: Express 15.712 with bar on 12 in p/q form.

Solution:

Let x=15.71212... →(1)

Multiply both sides by 100

100x=1571.212... →(2)

Subtract equation(1) from equation (2)

99x=1555.5

x=15555/990

x=3111/198

Final answer: 15.712 with bar on 12 =$\frac{3111}{198}$

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