Number System - Maharashtra Board STD 9 Maths Questions

Q 1MCQ(1M)1 Mark

Which of the following is rational?

A
$\sqrt{3}$
B
$\pi$
C
$\frac{4}{0}$
✓
$\frac{0}{4}$

Answer: D.

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Q 2MCQ(1M)1 Mark

An irrational number between $2$ and $2.5$ is:

A
$\sqrt{11}$
✓
$\sqrt{5}$
C
$\sqrt{22.5}$
D
$\sqrt{12.5}$

Answer: B.

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Q 3MCQ(1M)1 Mark

The number $0.\overline{32}$ when expressed in the form $\frac{\text{p}}{\text{q}}\ \big(p, q$ are integers and $\text{q}\neq0\big),$ is:

A
$\frac{8}{25}$
✓
$\frac{29}{90}$
C
$\frac{32}{99}$
D
$\frac{32}{199}$

Answer: B.

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Q 4MCQ(1M)1 Mark

Which one of the following statements is true?

A
The sum of two irrational numbers is always an irrational number.
B
The sum of two irrational numbers is always a rational number.
✓
The sum of two irrational numbers may be a rational number or an irrational number.
D
The sum of two irrational numbers is always an integer.

Answer: C.

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Q 5MCQ(1M)1 Mark

The number $1.\overline{27}$ in the form $\frac{\text{p}}{\text{q}},$ where $p$ and $q $ are integers and $\text{q}\neq0,$ is:

A
$\frac{14}{9}$
✓
$\frac{14}{11}$
C
$\frac{14}{13}$
D
$\frac{14}{15}$

Answer: B.

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Q 6Fill in the Blanks.1 Mark

The decimal representation of a rational number is either _______ or ________.

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Q 7Fill in the Blanks.1 Mark

The decimal form of an irrational number is neither ______ nor ______.

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Q 8Fill in the Blanks.1 Mark

Every point on the number line corresponds to a ______ number which many be either ______ or ______.

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Q 9Fill in the Blanks.1 Mark

Every real number is either ________ number or ________ number.

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Q 10True False With Reason2 Marks

Answer whether the following statements are true or false? Give reasons in support of your answer.
Every rational number is a whole number.

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Q 11True False With Reason2 Marks

Answer whether the following statements are true or false? Give reasons in support of your answer.
Every integer is a whole number.

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Q 12True False With Reason2 Marks

Answer whether the following statements are true or false? Give reasons in support of your answer.
Every rational number is an integer.

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Q 13True False With Reason2 Marks

Find whether the following statement are true or false:
Every real number is either rational or irrational.

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Q 14True False With Reason2 Marks

Answer whether the following statements are true or false? Give reasons in support of your answer.
Every whole number is a natural number.

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Q 151 Mark Question1 Mark

Express the following decimals in the form $\frac{\text{p}}{\text{q}}:$
7.010

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Q 161 Mark Question1 Mark

Express the following decimals in the form $\frac{\text{p}}{\text{q}}:$
9.90

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Q 171 Mark Question1 Mark

Give an example of two irrational numbers whose:
Quotient is an irrational number.

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Q 181 Mark Question1 Mark

Examine, whether the following numbers are rational or irrational:$\big(\sqrt{2}-2\big)^2$

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Q 191 Mark Question1 Mark

In the following equations, find which variables x, y and z etc. represent rational or irrational numbers:
$y^2=9$

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Q 202 Mark Question2 Marks

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

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Q 212 Mark Question2 Marks

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

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Q 222 Mark Question2 Marks

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

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Q 232 Mark Question2 Marks

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

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Q 242 Mark Question2 Marks

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

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Q 253 Mark Question3 Marks

Express the following decimals in the form $\frac{\text{p}}{\text{q}}:$$0.\bar{4}$

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Q 263 Mark Question3 Marks

Express the following decimals in the form $\frac{\text{p}}{\text{q}}:$$0.\overline{54}$

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Q 273 Mark Question3 Marks

Express the following decimals in the form $\frac{\text{p}}{\text{q}}:$$125.\bar{3}$

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Q 283 Mark Question3 Marks

Explain how irrational number is differ from rational numbers?

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Q 293 Mark Question3 Marks

Express the following decimals in the form $\frac{\text{p}}{\text{q}}:$$0.\overline{47}$

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Q 304 Mark Question4 Marks

Visualise the representation of $5.3\bar{7}$ on the number line upto 5 decimal places, that is upto 5.37777.

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Q 314 Mark Question4 Marks

Represent $\sqrt{3.4},\sqrt{9.4},\sqrt{10.5}$ on the real number line.

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Q 324 Mark Question4 Marks

Represent $\sqrt{6},\sqrt{7},\sqrt{8}$ on the number line.

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Q 334 Mark Question4 Marks

Find a rational number and also an irrational number lying between the numbers 0.3030030003... and 0.3010010001...

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Q 344 Mark Question4 Marks

Visualise $2.665$ on the number line, using successive magnification.

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