Tag: first forms

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Questions Related to first forms

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

$\dfrac{p}{q}$ form of the number $0.\overline{3}$ is :

  1. $\dfrac{3}{10}$
  2. $\dfrac{3}{100}$
  3. $\dfrac{1}{3}$
  4. $\dfrac{1}{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let $x$ = .33333......

Multiplying by 10 on both sides we get
$10x=3.3333....\ on\quad subtracting\quad both\quad equations\quad we\quad get,\ 9x=3\ x=\dfrac { 1 }{ 3 } $
So, correct answer is option C.

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

The decimal representation of $\dfrac { 93 }{ 1500 }$  will be

  1. Terminating

  2. Non-terminating

  3. Non-terminating, repeating

  4. Non-terminating, non-repeating
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Checking the termination of $\cfrac{93}{1500}$ is same as checking the termination of $\cfrac{31}{500}$ which is equal to $\cfrac{62}{1000}$


As the value is $0.062$, we can say the fraction is terminating.

$\therefore \cfrac{93}{1500}$ is terminating.

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

The fraction, $\dfrac{1}{3}$

  1. equals $0.33333333$
  2. is less than $0.33333333\ by\ \dfrac{1}{3.10^{8}}$
  3. is less than $0.33333333\ by\ \dfrac{1}{3.10^{9}}$
  4. is greater than $0.33333333\ by\ \dfrac{1}{3.10^{8}}$
  5. is greater than $0.33333333\ by\ \dfrac{1}{3.10^{9}}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\cfrac { 1 }{ 3 } -0.33333333=\cfrac { 1 }{ 3 } -\cfrac { 33333333 }{ { 10 }^{ 8 } } \ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad =\cfrac { { 10 }^{ 8 }-99999999 }{ 3\cdot { 10 }^{ 8 } } \ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad =\cfrac { 1 }{ 3\cdot { 10 }^{ 8 } } $

$\therefore \cfrac { 1 }{ 3 } $ is greater than 0.33333333 by $\cfrac { 1 }{ 3\cdot { 10 }^{ 8 } } $.

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

Let $x=\dfrac { p }{ q } $ be a rational number, such that the prime factorization of $q$ is of the form $2^n 5^m$, where $n, m$ are non-negative integers. Then $x$ has a decimal expansion which terminates.

  1. True

  2. False

  3. Neither

  4. Either
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The form of q is $2^n*5^m$
q can be $1,2,5,10,20,40....$
Any integer divided by these numbers will always give a terminating decimal number.

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

Without actually performing the long division, state whether the following rational number will have terminating decimal expansion or a non-terminating repeating decimal expansion. Also, find the numbers of places of decimals after which the decimal expansion terminates.
$\dfrac { 13 }{ 3125 } $

  1. $3$
  2. $4$
  3. $5$
  4. $6$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The given value is $\dfrac{13}{3125}$ the denominator is 3125 which can be written as:


$3125=2^0 \times 5^5$ it is in the form of $2^m \times 5^n$

$max(m,n)=5$

$\therefore$ the expansion is terminating decimal it terminates after 

$max(m,n)=5$ places from the decimal [since  $ m=0,n=5$]

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

State whether the following statement is true/false.

$\dfrac{2375}{375}$ is not a terminating decimal

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For $\cfrac{2375}{375}$


$375=5^3\times 3$ and $2375=5^3\times 19$


Since, denominator contains $3$ as a factor other than only $2$ or $5$,

So, $\cfrac{2375}{375}$ is is non terminating.