This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Real Numbers and their Decimal Expansions”.

1. Which of the following is the correct way to write \(5.4\bar{12}\)?

a) 5.412412412…

b) 5.4121212…

c) -5.412

d) 5.4 – 12

View Answer

Explanation: Bar sign is used to show the blocks of numbers which are repeated. Here, the sign of ‘bar’ ( ̅ ) is only over two numbers, 1 and 2 which means block of these two numbers is repeated infinite times. There is no sign of bar over ‘4’ which shows that ‘4’ is not repeated.

2. 0.3454545…..=_____________

a) 345/1000

b) 350/995

c) 355/900

d) 342/990

View Answer

Explanation: Let 0.3454545…=x

Then, 100x=34.54545…..

100x=34.2 + 0.3454545…

100x=34.2 + x

99x=34.2

Then, x=34.2/99

x=342/990.

3. The decimal expansion of rational numbers is either terminating or non-terminating and recurring (repeating).

a) True

b) False

View Answer

Explanation: Let’s take a known rational number to understand this.

For example, 3/4

We know that 3/4 is a rational number because both 3 and 4 are natural

numbers and 3/4=0.75 which is terminating expansion.

Now, let’s take one example of non-terminating and recurring expansion.

For example 0.5787878…

Let x=0.5787878…

Then 100x=57.878787…

100x=57.3 + 0.5787878…

100x=57.3 + x

99x=57.3

Then, x=57.3/99

x=573/990

This is of the form of p/q where p and q are natural numbers. Hence we can say that .5787878… is rational number.

Hence, we can conclude that the decimal expansion of rational numbers is either terminating or non-terminating and recurring (repeating).

We can also conclude that ‘The decimal expansion of irrational numbers is non-terminating and non-recurring.’

4. 0.3333… is a/an ______________

a) natural number

b) whole number

c) rational number

d) irrational number

View Answer

Explanation: Let 0.333…=x

Then, 10x=3.33333…

10x=3 + 0.333…

10x=3 + x

9x=3

Then, x=3/9=1/3

This is of the form p/q where p and q are natural numbers. Hence by definition, 0.3333…. is a rational number.

Another method: Decimal expansion of rational numbers is either terminating or non-terminating and recurring (repeating).

As we can see that 0.3333… is non-terminating and recurring so it is a rational number.

5. 0.238765563246… is a/an __________

a) rational number

b) irrational number

c) natural number

d) whole number

View Answer

Explanation: Given number is not an integer, so it does not belong to natural number and whole number set.

It is not-terminating and non-recurring, so we can say that 0.238765563246…is an irrational number and not a rational number.

6. Which of the following number is an irrational number between 1/3 and 2/3?

a) 0.3333….

b) 0.343403400…

c) 0.55555….

d) 0.67670671….

View Answer

Explanation: 1/3=0.3333… and 2/3=0.6666…0.333… and 0.555… are non-terminating and recurring, so they can be represented in the form p/q where p and q are integers. Hence they are rational numbers. 0.343403400 and 0.67670671… are non-terminating and non-recurring. Hence they are irrational numbers. But, among 0.343403400…and 0.67670671, only 0.343403400 is between 1/3 and 2/3. So option 0.343403400… is correct.

7. There are infinite irrational numbers between two numbers.

a) True

b) False

View Answer

Explanation: Let’s take any two numbers to understand this.

For example, 3/4 and 4/5

We know that 3/4=0.75 and 4/5=0.8

For a number to be irrational, it has to be non-terminating and non-recurring.

We can find infinite numbers between 0.75 and 0.8 which are non-terminating and non-recurring.

Like 0.756757758…., 0.78754729… and so on.

8. √5 is a/an ___________

a) natural number

b) whole number

c) rational number

d) irrational number

View Answer

Explanation: √5=2.236067…

This is not an integer, so it doesn’t belong to natural and whole number set by definition. Moreover, expansion of √5 is non-terminating and non-recurring. Hence, it is an irrational number.

**Sanfoundry Global Education & Learning Series – Mathematics – Class 9**.

To practice all areas of Mathematics, __ here is complete set of 1000+ Multiple Choice Questions and Answers__.

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