Decimal Expansion of Rational and Irrational Numbers

Q.

Without actual division, find which of the following rational numbers are terminating decimals. (i) $\frac{13}{80}$ (ii) $\frac{7}{24}$ (iii) $\frac{5}{12}$ (iv)$\frac{31}{375}$ (v) $\frac{16}{125}$

Q.

Express $0.12\overline{3}$ in the form of $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$.

Q.

Question 1 (i)
Write$\frac{36}{100}$ in decimal form and say what kind of decimal expansion it has.

Q.

Which of the following numbers can be represented as non-terminating, repeating decimals?

1. $\frac{3}{16}$

2. $\frac{137}{25}$

3. $\frac{39}{24}$

4. $\frac{3}{11}$

Q.

The smallest rational number by which $\frac{1}{3}$ should be multiplied so that its decimal expansion terminates after one place of decimal is:

1. $\frac{1}{10}$

2. $\frac{3}{10}$

3. 3

4. 30

Q.

If $x=0.\overline{17}$, then which of the following statements are true?

(i) $100x=17.\overline{17}$
(ii) $100x-x=16.\overline{17}$
(iii) $99x=17$

1. (i) only
2. (i) and (iii)
3. (i) and (ii)
4. (i), (ii) and (iii)

Q.

Which of the following is an irrational number?

i) $2\sqrt{3}$

ii) $0.143\overline{32}$

iii) $5.\overline{46}$

iv) $\sqrt{5}$

1. All of the above

2. Only iv)

3. ii) and iii)

4. i) and iv)

Q.

The decimal expansion of the number $\sqrt{2}$ is _______?

Q.

The number 0.318564318564318564.... is:

1. a natural number

2. an integer

3. a rational number

4. an irrational number

Q.

Why is 22/7 non terminating and non recurring even though it is a rational number in p/q form?

Q.

Express the following rational numbers as decimals:

(i) $\frac{2}{3}$ (ii) - $\frac{4}{9}$ (iii) $\frac{-2}{15}$ (iv) $\frac{22}{13}$ (v) $\frac{437}{999}$ (vi) $\frac{33}{26}$

Q.

How many digits are there in the repeating block of digits in the decimal expansion of $\frac{17}{7}$

(a) 16

(b) 6

(c) 26

(d) 7

Q.

The decimal representation of a rational number is

(a) always terminating (b) either terminating or repeating

(c) either terminating or nonrepeating (d) neither terminating nor-repeating

Q. Express each of the following decimals in the form $\frac{p}{q}:$
(i) $0.\overline{4}$

(ii) $0.\overline{37}$

(iii) $0.\overline{54}$

(iv) $0.\overline{621}$

(v) $125.\overline{3}$

(vi) $4.\overline{7}$

(vii) $0.\overline{47}$

Q.

In the distributed version control system, developers can clone the central code base to their local system.

Q.

The number $\frac{665}{625}$ will terminate after how many decimal places?

Q. Find the decimal form of $\frac{7}{8}$.

Q. The value of $3.\overline{42}+8.\overline{053}$ is equal to

1. $\frac{1733}{150}$
2. $\frac{5231}{450}$
3. $\frac{5143}{495}$
4. $\frac{3787}{330}$

Q.

The decimal expansion that a rational number cannot have is

(a) 0.25

(b) $0.25\overline{28}$

(c)$0.\overline{2528}$

(d) 0.5030030003...

Q.

Which of the following are irrational number?

i) $2\sqrt{3}$

ii) $0.143\overline{32}$

iii) $5.\overline{46}$

iv) $\sqrt{5}$

1. Only iv
2. i and iv
3. Only iii
4. ii and iii

Q. Find whether the following statement are true or false.
(i) Every real number is either rational or irrational.
(ii) $\pi$ is an irrational number.
(iii) Irrational numbers cannot be represented by points on the number line.

Q. Represent $\sqrt{9.3}$ on the number line.

Q. Express each of the following as a fraction in simplest form.
(i) $0.\overline{3}$
(ii) $1.\overline{3}$
(iii) $0.\overline{34}$
(iv) $3.\overline{14}$
(v) $0.\overline{324}$
(vi) $0.\overline{17}$
(vii) $0.\overline{54}$
(viii) $0.\overline{163}$

Q. Write each of the following in decimal form and say what kind of decimal expansion each has. (i) $\frac{5}{8}$ (ii) $\frac{7}{25}$ (iii) $\frac{3}{11}$ (iv)$\frac{5}{13}$ (v) $\frac{11}{24}$ (vi)$\frac{261}{400}$ (vii) $\frac{231}{625}$ (viii)$2\frac{5}{12}$

Q.

_______Is The Process Of Finding Errors In Software Code

Q.

Write each of the following as decimals.

$\left(d\right)23+\frac{2}{10}+\frac{6}{1000}$

Q.

Insert a rational number and an irrational number between $3.623623$ and $0.484848$

Q.

Express $26$ $\mathrm{kg}$ $50$ $\mathrm{g}$ as $\mathrm{kg}$ using decimals

Q.

The decimal expansion of $\sqrt{2}$ is

(a) finite decimal

(b) 1.4121

(c) non terminating recurring

(d) non terminating, non recurring

Q.

Complete the following sentences:

(i) Every point on the number line corresponds to a ....... number which may be either be ...... or ....

(ii) The decimal form of an irrational number is neither ... nor ...

(iii) The decimal representation of a rational number is either ... number or ... number.

(iv) Every real number is either ... number or ... number