Tag: maths

Questions Related to maths

Which one of the following is not a correct statement ?

maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

  1. $\displaystyle 0.\overline{01}=\frac{1}{90}$

  2. $\displaystyle 0.\overline{1}=\frac{1}{9}$

  3. $\displaystyle 0.\overline{2}=\frac{2}{9}$

  4. $\displaystyle 0.\overline{3}=\frac{1}{3}$

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Correct Option: A
Explanation:

$\dfrac{1}{90} = 0.0111111111 = 0.0\bar{1}$


$\dfrac{1}{9} = 0.11111111 = 0.\bar{1}$

$\dfrac{2}{9} = 0.222222222 = 0.\bar{2}$

$\dfrac{1}{3} = 0.3333333333= 0.\bar{3}$

Hence, option $A$ is not correct.

The decimal form of $5\dfrac{3}{8}$ is

maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

  1. $5.375$

  2. $5.000$

  3. $5.255$

  4. $2.325$

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Correct Option: A
Explanation:

First change the mixed fraction into proper fraction.
$5\dfrac{3}{8}=\dfrac{43}{8}$

$\dfrac{43}{8}= 5 + \dfrac38 = 5 + 0.375 = 5.375$

Arrange the following decimal numbers in ascending order.
$5.5, 0.55, 0.055, 0.005$

maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

  1. $5.5, 0.055, 0.005, 0.55$

  2. $0.55, 0.005, 0.055, 5.5$

  3. $5.5, 0.55, 0.055, 0.005$

  4. $0.005, 0.055, 0.55, 5.5$

Show answer
Correct Option: D
Explanation:

We need to arrange the numbers from smallest to largest.
So, $0.005, 0.055, 0.55, 5.5$ is in ascending order

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

maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

  1. Integers

  2. Whole

  3. Rational

  4. Irrational

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Correct Option: C
Explanation:

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


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

Both are rational numbers but it was non repeating then they are irrational numbers.
Therefore, $C$ is the correct answer.

If the denominator of a fraction has factors other then $2$ and $5$, the decimal expression ..............

maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

  1. repeats

  2. is that of a whole number

  3. has equal numerator and denominator

  4. terminates

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Correct Option: A
Explanation:

If there are prime factors in the denominator other than $2$ or $5$, then the decimals repeat.
$\dfrac {1}{24} = \dfrac {1}{3\times 2\times 2\times 2}$ (there is a factor of $3$, the decimal will repeat.)
Therefore, $A$ is the correct answer.

If the denominator of a fraction has only factors of $2$ and factors of $5$, the decimal expression ............. 

maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

  1. has equal numerator and denominator

  2. becomes a whole number

  3. does not terminate

  4. terminates

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Correct Option: D
Explanation:

When the prime factorization of the denominator of a fraction has only factors of $2$ and factors of $5$, we can always express the decimal as terminating decimal. 
For examples $\dfrac {1}{25} = \dfrac {1}{5\times 5}$ repeats (just powers of $5$, the decimal terminates.)
Therefore, $D$ is the correct answer.

$\dfrac {1}{2} = 0.5$
It is a terminating decimal because the denominator has a factor as ...........

maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

  1. $0$

  2. $1$

  3. $2$

  4. $6$

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Correct Option: C
Explanation:

If the prime factors in the denominator of a fraction has factors of $2$ and $5$, then the decimals terminate. The denominator has $2$ as a factor.
Therefore, $C$ is the correct answer.


$\dfrac {17}{8}$ can be expressed as $.....$. It is a $........$ decimal.
maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

  1. $ 2.125$, terminating

  2. $ 2.321321...$, non-terminating

  3. $1.125125124...$, recurring

  4. $2.125$, irrational

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Correct Option: A
Explanation:

$\dfrac {17}{8}=\dfrac{17\times125}{8\times 125}=  \dfrac{2125}{1000}=2.125$

When the division process does not end and the remainder is not equal to zero; then such decimal is known as ............... decimal

maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

  1. terminating

  2. non-terminating

  3. recurring

  4. irrational

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Correct Option: B
Explanation:

The division is completed when we get the remainder zero. In this division process we do not get a zero and it is never ending. This process of division is called a non- terminating decimal.
Therefore, $B$ is the correct answer.

Which of the following fractions will terminate when expressed as a decimal? (Choose all that apply.)

maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

  1. $\frac{1}{256}$

  2. $\frac{27}{100}$

  3. $\frac{100}{27}$

  4. $\frac{231}{660}$

  5. $\frac{7}{105}$

Show answer
Correct Option: A,B,D
Explanation:

Recall that in order for the decimal version of a fraction to terminate, the fraction's denominator in fully reduced form must have a prime factorization that consists of only 2's and/or 5's. 

The denominator in (A) is composed of only 2's $(256 = 2^8)$. 
The denominator in (B) is composed of only 2's and 5's $(100=2^2\times 5^2)$. 
In fully reduced form, the fraction in (D) is equal to $\frac{7}{20}$ and 20 is composed of only 2's and 5's $(20=2^2\times 5)$.
 By contrast, the denominator in (C) has prime factors other than Z's and 5's $(27 =3^3)$, and in fully reduced form, the fraction in (E) is equal to $\frac{1}{15}$, and 15 has a prime factor other than 2's and 5's $(15 = 3 \times 5)$.