Number Systems Test

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Number Systems Test - 32

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following is irrational?

A
$$\displaystyle\frac{1}{3}$$

B
$$\displaystyle\frac{48}{5}$$

C
$$0.7777\dots$$

D
$$1.73202002\dots$$

Solution

$$\textbf{Step -1: Definition of irrational numbers.}$$
$$\text{Numbers that cannot be represented in }\dfrac{p}{q}\text{ form are said to be irrational numbers.}$$

$$\text{Irrational numbers are non-repeating and non-terminating decimal numbers.}$$

$$\textbf{Step -2: Using the definition find the answer.}$$
$$\text{Some examples of irrational numbers are }\sqrt{2}, \sqrt{3}, \pi, 6.9318786..., \text{etc}.$$

$$\therefore \text{1.73202002... is a non-repeating and non-terminating number, hence is an irrational number.}$$

$$\textbf{Hence, among the following options, (D) 1.73202002... is an irrational number.}$$
Question 2
1 / -0

$$\dfrac {17}{8}$$ can be expressed as $$.....$$. It is a $$........$$ decimal.

A
$$ 2.125$$, terminating

B
$$ 2.321321...$$, non-terminating

C
$$1.125125124...$$, recurring

D
$$2.125$$, irrational

Solution

$$\dfrac {17}{8}=\dfrac{17\times125}{8\times 125}= \dfrac{2125}{1000}=2.125$$,
which is terminating.
Therefore, option $$A$$ is the correct answer.
Question 3
1 / -0

............... numbers have terminating and non- terminating repeating decimals.

A
Integers

B
Whole

C
Rational

D
Irrational

Solution

$$\dfrac {1}{4} = 0.25$$ is a terminating decimal.

$$\dfrac {8}{3} = 2.666666666......$$ is a non-terminating repeating decimal.

Both are rational numbers as both can be represented in the form of $$\dfrac{p}{q}$$.

Therefore, $$C$$ is the correct answer.
Question 4
1 / -0

What rational number lies exactly halfway between $$\dfrac{2}{3}$$ and $$\dfrac{3}{4}$$?

A
$$\dfrac{3}{5}$$

B
$$\dfrac{5}{6}$$

C
$$\dfrac{7}{12}$$

D
$$\dfrac{9}{16}$$

E
$$\dfrac{17}{24}$$

Solution

Consider $$3 \times 4 = 12$$,

So, $$\dfrac {2}{3} = \dfrac{8}{12}$$

$$\dfrac 34 = \dfrac{9}{12}$$

Multiplying the numerator and denominator by $$2$$:

$$\dfrac{16}{24}$$ and $$\dfrac{18}{24}$$.

The mid point is $$\dfrac{17}{24}$$

Hence option $$E$$ is correct.
Question 5
1 / -0

Consider the following statements:
1. $$\dfrac {1}{22}$$ cannot be written as a terminating decimal.
2. $$\dfrac {2}{15}$$ can be written as a terminating decimal.
3. $$\dfrac {1}{16}$$ can be written as a terminating decimal.
Which of the statements given above is/are correct?

A
$$1$$ only

B
$$2$$ only

C
$$3$$ only

D
$$2$$ and $$3$$

Solution

$$\dfrac{1}{22}$$ is an irrational number hence it is a non terminating number
$$\dfrac{2}{15}$$ is an irrational number hence it is a non terminating number
$$\dfrac{1}{16}$$ is an rational number hence it is a terminating number
Question 6
1 / -0

Calculate the number of irrational numbers between $$1$$ and $$8$$.

A
Fewer than $$3$$

B
$$3$$

C
$$6$$

D
$$7$$

E
More than $$7$$

Solution

Between any two rational numbers there are infinite number of irrational numbers. Hence, the required answer is more than $$7$$.
Question 7
1 / -0

How many irrational numbers are there between $$2$$ and $$6$$?

A
$$1$$

B
$$3$$

C
$$4$$

D
$$10$$

E
Infinitely many

Solution

There can be infinite number of irrational numbers between any two rational numbers.

Hence, $$Op-E$$ is correct.
Question 8
1 / -0

Identity the rational number that does not lie between $$ \cfrac{3}{5}$$ and $$ \cfrac{2}{3}$$.

A
$$ \cfrac{46}{75}$$

B
$$ \cfrac{47}{75}$$

C
$$ \cfrac{49}{75}$$

D
$$ \cfrac{50}{75}$$
Question 9
1 / -0

Identify the rational numbers from the followings:
$$72, \dfrac {5}{27}, \dfrac {62}{0}, 1\dfrac {3}{5}, -7\dfrac {5}{4}, 0$$

A
All are rational numbers

B
All except $$\dfrac {62}{0}$$ and $$0$$

C
All except $$1\dfrac {3}{5}, -7\dfrac {5}{4}$$

D
All except $$\dfrac {62}{0}$$

Solution

All written in the form of fraction and we know that all fraction are rational number except those having denominator as 0 because having denominator 0 makes function undefined.
So correct answer will be option D
Question 10
1 / -0

In mathematics, the irrational number e $$= 2.718$$... Which of the following letters corresponds to the number e on the number line below?

A
A

B
B

C
C

D
D

Solution

Since the part between $$2.70$$ and $$2.75$$ is divided into $$5$$ parts , so, each part measures $$0.01$$.
$$e=2.718$$ is to be located on the number line.
So, on analysis, we can say that point B is the correct point.

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Number Systems Test - 32

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Number Systems Test - 32

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Question 1

$$\displaystyle\frac{1}{3}$$

$$\displaystyle\frac{48}{5}$$

$$0.7777\dots$$

$$1.73202002\dots$$

Solution

Question 2

$$ 2.125$$, terminating

$$ 2.321321...$$, non-terminating

$$1.125125124...$$, recurring

$$2.125$$, irrational

Solution

Question 3

Integers

Whole

Rational

Irrational

Solution

Question 4

$$\dfrac{3}{5}$$

$$\dfrac{5}{6}$$

$$\dfrac{7}{12}$$

$$\dfrac{9}{16}$$

$$\dfrac{17}{24}$$

Solution

Question 5

$$1$$ only

$$2$$ only

$$3$$ only

$$2$$ and $$3$$

Solution

Question 6

Fewer than $$3$$

$$3$$

$$6$$

$$7$$

More than $$7$$

Solution

Question 7

$$1$$

$$3$$

$$4$$

$$10$$

Infinitely many

Solution

Question 8

$$ \cfrac{46}{75}$$

$$ \cfrac{47}{75}$$

$$ \cfrac{49}{75}$$

$$ \cfrac{50}{75}$$

Question 9

All are rational numbers

All except $$\dfrac {62}{0}$$ and $$0$$

All except $$1\dfrac {3}{5}, -7\dfrac {5}{4}$$

All except $$\dfrac {62}{0}$$

Solution

Question 10

A

B

C

D

Solution

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