2 Marks Questions - Maths STD 9 Questions - Vidyadip

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21 questions · timed · auto-graded

Question 12 Marks

Look at several examples of rational numbers in the form $\frac{\text{p}}{\text{q}}(\text{q}\neq0),$ where p and q are integers with no common factors other than 1 and having terminating decimal representations. Can you guess what property q must satisfy?

Answer

A rational number $\frac{\text{p}}{\text{q}}$ is a terminating decimal only, when prime factors of q are 2 and 5 only. Therefore, $\frac{\text{p}}{\text{q}}$ is a terminating decimal only, when prime factorization if q must have only powers of 2 or 5 or bith.

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Question 22 Marks

Is zero is rational number? Can you write it in the form $\frac{\text{p}}{\text{q}},$ where p and q are integers and $\text{q}\neq0?$

Answer

Yes, zero is a rational number. It can be written in the form of $\frac{\text{p}}{\text{q}}$ where $\text{q}\neq0$ as such as $\frac{0}{3},\frac{0}{5},\frac{0}{11}, \ \text{etc }...$

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Question 32 Marks

In the following equations, find which variables x, y and z etc. represent rational or irrational numbers:
z² = 0.04

Answer

z² = 0.04
We have,
Taking square root on the both sides, we get
z = 0.2
$\frac{2}{10}$ can be expressed in the form of $\frac{\text{a}}{\text{b}},$ so it is a rational number.

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Question 42 Marks

In the following equations, find which variables x, y and z etc. represent rational or irrational numbers:
x² = 5

Answer

We have,
x² = 5
Taking square root on both the sides, we get
$\text{x}=\sqrt{5}$
$\sqrt{5}$ is not a perfect square root, so it is an irrational number.

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Question 52 Marks

In the following equations, find which variables x, y and z etc. represent rational or irrational numbers:
$\text{v}^2=3$

Answer

We have,
$\text{v}^2=3$
Taking square root on both sides, we get,
$\text{v}=\sqrt{3}$
$\sqrt{3}$ is not a perfect square root, so v is irrational number.

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Question 62 Marks

In the following equations, find which variables x, y and z etc. represent rational or irrational numbers:
$\text{u}^2=\frac{17}{4}$

Answer

We have,
$\text{u}^2=\frac{17}{4}$
Taking square root on both sides, we get,
$\text{u}=\sqrt{\Big(\frac{17}{4}\Big)}$
$\text{u}=\Big(\frac{\sqrt{17}}{4}\Big)$
Quotient of an irrational and a rational number is irrational, so u is an Irrational number.

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Question 72 Marks

Identify the following as rational or irrational numbers. Give the decimal representation of rational numbers:
$\sqrt{\Big(\frac{9}{27}\Big)}$

Answer

We have,
$\sqrt{\Big(\frac{9}{27}\Big)}$
$=\frac{3}{\sqrt{27}}$
$=\frac{1}{\sqrt{3}}$
Quotient of a rational and an irrational number is irrational numbers so $\frac{1}{\sqrt{3}}$ is an irrational number.
$\sqrt{\Big(\frac{9}{27}\Big)}$ is an irrational number.

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Question 82 Marks

Identify the following as rational or irrational numbers. Give the decimal representation of rational numbers:
$-\sqrt{64}$

Answer

We have,
$-\sqrt{64}$
$=-8$
$=-\Big(\frac{8}{1}\Big)$
$=-\Big(\frac{8}{1}\Big)$ can be expressed in the form of $\frac{\text{a}}{\text{b}},$
so $-\sqrt{64}$ is a rational number.
Its decimal representation is -8.0.

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Question 92 Marks

Identify the following as rational or irrational numbers. Give the decimal representation of rational numbers:
$\sqrt{4}$

Answer

We have,
$\sqrt{4}$ can be written in the form of
$\frac{\text{p}}{\text{q}}.$ So, it is a rational number. Its decimal representation is 2.0

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Question 102 Marks

Identify the following as rational or irrational numbers. Give the decimal representation of rational numbers:
$\sqrt{1.44}$

Answer

We have,
$\sqrt{1.44}$
$=\sqrt{\Big(\frac{144}{100}\Big)}$
$=\frac{12}{10}$
$=1.2$
Every terminating decimal is a rational number, so 1.2 is a rational number. Its decimal representation is 1.2.

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Question 112 Marks

Identify the following as rational or irrational numbers. Give the decimal representation of rational numbers:
$\sqrt{100}$

Answer

We have,
$\sqrt{100}$
= 10 can be expressed in the form of $\frac{\text{a}}{\text{b}},$
So $\sqrt{100}$ is a rational number
Its decimal representation is 10.0.

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Question 122 Marks

Identify the following as rational or irrational numbers. Give the decimal representation of rational numbers:
$3\sqrt{18}$

Answer

We have,
$3\sqrt{18}$
$=3\times\sqrt{2}\times3\times3$
$=9\times\sqrt{2}$
Since, the product of a ratios and an irrational is an irrational number.
$=9\times\sqrt{2}$ is an irrational.
$=3\times\sqrt{18}$ is an irrational number.

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Question 132 Marks

Express the following rational numbers as decimals:
$-\frac{4}{9}$

Answer

Given rational number is $-\frac{4}{9}$

Now we have to express this rational number into decimal form. So We will use long division method as below.

Therefore $\frac{4}{9}=0.444$

$\Rightarrow-\frac{4}{9}=0.\bar{4}$

Hence, $-\frac{4}{9}=-0.\bar{4}$

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Question 142 Marks

Express the following rational numbers as decimals:
$\frac{437}{999}$

Answer

Given rational number is $\frac{437}{999}$

Now we have to express this rational number into decimal form. So We will use long division method as below.

Therefore $\frac{2}{13}=1.692307$

$\Rightarrow\frac{22}{33}=\overline{1.692307}$

Hence, $\frac{-22}{13}-0.\overline{1692307}$

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Question 152 Marks

Express the following rational numbers as decimals:
$\frac{42}{100}$

Answer

Given rational number is $\frac{42}{100}$
Now we have to express this rational number into decimal form. We will use long division method as below.

Hence, $\frac{42}{100}=0.42$

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Question 162 Marks

Express the following rational numbers as decimals:
$\frac{33}{26}$

Answer

By long division, we have

$\therefore\frac{33}{26}=1.2692307698307\ ...=1.\overline{2692307}$

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Question 172 Marks

Express the following rational numbers as decimals:
$\frac{327}{500}$

Answer

Given rational number is $\frac{327}{500}$

Now we have to express this rational number into decimal form. So We will use long division method as below.

Hence, $\frac{327}{500}=0.654$

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Question 182 Marks

Express the following rational numbers as decimals:
$\frac{2}{3}$

Answer

Given rational number is $\frac{2}{3}$

Now we have to express this rational number into decimal form. So We will use long division method as below.

Therefore $\frac{2}{3}=0.6666$

$\Rightarrow\frac{2}{3}=0.\bar{6}$

Hence, $\frac{2}{3}=0.\bar{6}$

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Question 192 Marks

Express the following rational numbers as decimals:
$-\frac{22}{13}$

Answer

Given rational number is $-\frac{22}{13}$

Now we have to express this rational number into decimal form. So We will use long division method as below.

Therefore $\frac{2}{13}=1.692307$

$\Rightarrow\frac{22}{33}=\overline{1.692307}$

Hence, $\frac{-22}{13}-0.\overline{1.692307}$

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Question 202 Marks

Express the following rational numbers as decimals:
$\frac{-2}{15}$

Answer

Given rational number is $\frac{-2}{15}$

Now we have to express this rational number into decimal form. So We will use long division method as below.

Therefore $\frac{2}{15}=0.13333$

$\Rightarrow\frac{2}{15}=0.\overline{13}$

Hence, $\frac{-2}{15}-0.\overline{13}$

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Question 212 Marks

Express the following rational numbers as decimals:
$\frac{15}{4}$

Answer

Given rational number is $\frac{15}{4}$

Now we have to express this rational number into decimal form. So We will use long division method as below.

Hence, $\frac{15}{4}=3.75$

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2 Marks Questions - Maths STD 9 Questions - Vidyadip