Tag: maths

Questions Related to maths

Identify a non-terminating repeating decimal.

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

  1. $\dfrac{24}{1600}$

  2. $\dfrac{171}{800}$

  3. $\dfrac{123}{2^2 \times 5^3}$

  4. $\dfrac{145}{2^3 \times 5^2 \times 7^2}$

Show answer
Correct Option: D
Explanation:

An fraction will be terminating decimal only if denominator will be in form of 

${2}^{m}\times{{5}^{n}}$. 
Now lets check denominator of each option 
Only option D does not satisfies this condition So it will be non terminating 
So correct answer will be option D

A rational number can be expressed as a terminating decimal if the denominator has factors _________.

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

  1. $2$ or $5$

  2. $2$, $3$ or $5$

  3. $3$ or $5$

  4. Only $2$ and $3$

Show answer
Correct Option: A
Explanation:

Any rational number its denominator is in the form of ${ 2 }^{ m }\times { 5 }^{ n }$,where m,n are positive integer s are terminating decimals.

So correct answer will be option A

Which one of the following has a terminating decimal expansion?

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

  1. $\displaystyle\frac{5}{32}$

  2. $\displaystyle\frac{7}{9}$

  3. $\displaystyle\frac{8}{15}$

  4. $\displaystyle\frac{1}{12}$

Show answer
Correct Option: A
Explanation:

We know that a terminating decimal is a decimal that ends. It's a decimal with a finite number of digits. For example $\dfrac {1}{4}=0.25$, it has only two decimal digits.


Now consider the fraction $\dfrac {5}{32}$ whose decimal form will be:

$\dfrac {5}{32}=0.15625$

The resulting decimal number ends with five decimal digits and therefore, it is terminating decimal.

Hence, $\dfrac {5}{32}$ has a terminating decimal expansion.

Which of the following numbers has the terminal decimal representation?

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

  1. $\dfrac{1}{7}$

  2. $\dfrac{1}{3}$

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

  4. $\dfrac{17}{3}$

Show answer
Correct Option: C
Explanation:
Option A: $\dfrac {1}{7}=0.1428..$
Option B: $\dfrac {1}{3}=0.3333....$
Option C: $\dfrac{3}{5}=0.6\Rightarrow $ terminal decimal number
Lets check option D : $\dfrac {17}{3}=5.6666...$
Hence, option C is correct.

A real number $\displaystyle \frac{2^2 \times 3^2 \times 7^2}{2^5 \times 5^3 \times 3^2 \times 7}$ will have _________.

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

  1. Terminating decimal

  2. Non-terminating decimal

  3. Non-terminating and non-repeating decimal

  4. Terminating repeating decimal

Show answer
Correct Option: A
Explanation:

$\dfrac{2^{2}\times3^{2}\times7^{2}}{2^{5}\times5^{3}\times3^{2}\times7} = 2^{2-5}\times3^{2-2}\times5^{-3}\times7^{2-1}$


                                 $= \dfrac{7}{2^{3}\times5^{3}}$

                                 $= \dfrac{7}{1000}$

                                 $= 0.007$
$0.007$ is a terminating non-repeating decimal

State the following statement is True or False

$\dfrac{987}{10500}$ will have terminating decimal expansion. 

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

Terminating decimal expansion, because

$ \dfrac{987}{10500}=\dfrac{329}{3500}=\dfrac{329}{2^2.5^3.7}=\dfrac{47}{2^2.5^3}=.094. $

Given that $\dfrac {1}{7} = 0.\overline {142857}$, which is a repeating decimal having six different digits. If $x$ is the sum of such first three positive integers $n$ such that $\dfrac {1}{n} = 0.\overline {abcdef}$, where $a, b, c, d, e$ and $f$ are different digits, then the value of $x$ is

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

  1. $20$

  2. $21$

  3. $41$

  4. $42$

Show answer
Correct Option: C
Explanation:

$1^{st}$ number
$x _{1} = 7$
$\Rightarrow \dfrac {1}{x _{1}} = 0.\overline {142857}$
such that,
$2^{nd}$ number
$x _{2} = 13$
$\Rightarrow \dfrac {1}{x _{2}} = 0.\overline {076923}$
$x _{3} = 21$
$\Rightarrow \dfrac {1}{x _{3}} = \dfrac {1}{21} = 0.\overline {047619}$
$x = x _{1} + x _{2} + x _{3}$
$\Rightarrow 7 + 13 + 21 = 41$.

If $x =\dfrac{p}{q}$  be a rational number such that the prime factorization of $q$ is not of the form $2^n 5^m$, where $n, m$ are non-negative integers. Then $x$ has a decimal expansion which is terminating.

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

  1. True

  2. False

  3. Neither

  4. Either

Show answer
Correct Option: B
Explanation:

If q is not of the form $2^n*5^m$ then definitely q can take any of the values 3,6,9,12,15,...etc.
As we know 4/3,20/6 all are non-terminating, thus required decimal expansion is non terminating.

The numbers 7.478478.... and 1.101001000100001.....are

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

  1. Rational and irrational respectively

  2. Both rationals

  3. Both irrationals

  4. None of these

Show answer
Correct Option: A
Explanation:

In 7.478478.......  we can see that after decimal the digits 478 are repeating itself again and again.

Hence it is a non-terminating and repeating decimal. Therefore it is a rational number.

In 1.101001000100001........  it is a non-terminating and non-repeating decimal.
Therefore it is an irrational number.
Hence option A is correct. 

The lottery method is_________.

maths frequency distribution tables and graphs introduction to statistics introduction to statistical method and econometrics partition values

  1. very expensive

  2. very easy

  3. time saving

  4. time consuming and cumbersome

Show answer
Correct Option: D
Explanation:

Lottery method can be time consuming if a large population or sample is involved in this and also it becomes a very tedious and ambiguous task.