Rational Numbers Test

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Rational Numbers Test - 19

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Question 1
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 2
1 / -0

Which number is represented by $$A$$, in the following number line?

A
$$13$$

B
$$\dfrac {6}{13}$$

C
$$6$$

D
$$\dfrac {0}{13}$$

Solution

In the given number line, every number increases by $$\dfrac {1}{13}$$ as we move right.
$$\therefore \dfrac {5}{13} + \dfrac {1}{13} = \dfrac {6}{13} \\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \dfrac {A}{13}$$
$$\therefore A = 6$$.
Question 3
1 / -0

Which number is represented by $$x$$, in the given number line?

A
$$-1$$

B
$$1$$

C
$$0$$

D
$$3$$

Solution

The numbers represented on the number line are ranging. $$\dfrac {-3}{3}, \dfrac {-2}{3}, \dfrac {-1}{3}, 0, \dfrac {1}{3}, \dfrac {2}{3}, .....$$ i.e. $$\dfrac {1}{3}$$ is added to every right element. Thus, $$x = \dfrac {-1}{3} + \dfrac {1}{3} = 0$$.
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

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 6
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 7
1 / -0

Out of the rational numbers $$\displaystyle\frac{5}{-11}, \frac{5}{-12}, \frac{5}{-17}$$, which is the greatest?

A
$$\displaystyle\frac{-5}{11}$$

B
$$\displaystyle\frac{5}{-12}$$

C
$$\displaystyle\frac{-5}{17}$$

D
Cannot be compared

Solution

$$\dfrac{5}{-11}=-0.45$$

$$\dfrac{5}{-12}=-0.42$$

$$\dfrac{5}{-17}=-0.29$$

Hence$$\dfrac{-5}{17}$$ is the greatest.
Question 8
1 / -0

Write the $$0.6$$ in $$\dfrac{p}{q}$$ form.

A
$$\dfrac3 7$$

B
$$\dfrac3 8$$

C
$$\dfrac3 5$$

D
$$\dfrac3 2$$

E
None of the above

Solution

Let $$x=0.6$$

$$\Rightarrow x=\dfrac{6}{10}=\dfrac{3}{5}$$ is a rational number.
Question 9
1 / -0

Find two rational numbers lying between $$\dfrac{-1}{3}$$ and $$\dfrac{1}{2}$$.

A
-1/6,1 /6

B
-2/3, 2/3

C
none

D
both

Solution
Question 10
1 / -0

The rational number that lies between $$\dfrac{3}{7}$$ and $$\dfrac{2}{3}$$ is

A
$$\dfrac{2}{5}$$

B
$$\dfrac{4}{7}$$

C
$$\dfrac{3}{7}$$

D
$$\dfrac{2}{3}$$

Solution

$$ \dfrac{3}{7}\times \dfrac{3}{3} = \dfrac{9}{21},$$

$$\dfrac{2}{3}\times \dfrac{7}{7} = \dfrac{14}{21} $$

Rational numbers between $$ \dfrac{3}{7} $$ & $$ \dfrac{2}{3} $$ are $$ \dfrac{10}{21},\dfrac{11}{21},\dfrac{12}{21},\dfrac{13}{21} $$

$$ \dfrac{12}{21}= \dfrac{4}{7} $$

Hence, $$ \dfrac{4}{7} $$ lies between $$\dfrac37$$ and $$\dfrac23$$.

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Rational Numbers Test - 19

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Rational Numbers Test - 19

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Question 1

Integers

Whole

Rational

Irrational

Solution

Question 2

$$13$$

$$\dfrac {6}{13}$$

$$6$$

$$\dfrac {0}{13}$$

Solution

Question 3

$$-1$$

$$1$$

$$0$$

$$3$$

Solution

Question 4

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

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

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

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

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

Solution

Question 5

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

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

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

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

Question 6

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 7

$$\displaystyle\frac{-5}{11}$$

$$\displaystyle\frac{5}{-12}$$

$$\displaystyle\frac{-5}{17}$$

Cannot be compared

Solution

Question 8

$$\dfrac3 7$$

$$\dfrac3 8$$

$$\dfrac3 5$$

$$\dfrac3 2$$

None of the above

Solution

Question 9

-1/6,1 /6

-2/3, 2/3

none

both

Solution

Question 10

$$\dfrac{2}{5}$$

$$\dfrac{4}{7}$$

$$\dfrac{3}{7}$$

$$\dfrac{2}{3}$$

Solution

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