Question

Classify 10.124124...... As rational or irrational with justification

Answer 1

Here, the decimal form of 10.124124124..... is non-terminating and recurring.

Thus, the number is rational.

It can be represented in p/q form as follows:

Let x = 10.124124... -------(1)

Multiplying 1000 on both sides,

∴1000x =10124.124124... -------(2)

Subtracting (1) from (2)
∴1000x - x = 10124.124124... - 10.124124...
∴999x = 10114
∴x = 10114/999

Thus, p/q form of the given decimal number is 10114/999.

Thus, the number is rational.

Answer 2

Answer:

non- terminating Rational Number