Question

Which of the following is an irrational number?
a.0.32bar
b. 0.321bar
c. 0. 321bar
d. 0.3232232223

Answer 1

D is the answer
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Answer 2

(d) 0.3232232223.. is an irrational number.

• Real numbers that are not exact fractions are known as irrational numbers.
• This means that ratios or complete fractions cannot accurately represent irrational values.
• Irrational numbers are non-terminating and have non-repeating decimal expansion.
• Irrational numbers cannot be readily compared to rational numbers using general arithmetic techniques.
• Options (a), (b), and (c) are rational numbers.
• Let's take the example of 0.32 bar.

0.32 bar = 0.32323232… = say x.

100 * x = 32.323232323……

100x - x = 32.323232323... - 0.32323232…

99 * x = 32

x = 32 / 99

Since this number can be expressed in the form A/B where A & B are integers & the value of B is not zero, this number, x is a rational number.

So, 0.32 bar is a rational number. Similarly, 0.321 bar is also rational.

• 0.3232232223.. is non-terminating and also non-recurring hence it is an irrational number.

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