Tag: first forms

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

Without doing any actual division, find which of the following rational numbers have terminating decimal representation :
(i) $\displaystyle \dfrac{7}{16}$ (ii) $\displaystyle \dfrac{23}{125}$
(iii) $\displaystyle \dfrac{9}{14}$ (iv) $\displaystyle \dfrac{32}{45}$
(v) $\displaystyle \dfrac{43}{50}$ (vi) $\displaystyle \dfrac{17}{40}$
(vii) $\displaystyle \dfrac{61}{75}$ (viii) $\displaystyle \dfrac{123}{250}$

  1. (i), (iii), (v), (vi) and (vii)

  2. (i), (ii), (v), (vi) and (viii)

  3. (i), (iii), (v), (vi) and (viii)

  4. (i), (ii), (v), (vi) and (vii)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

 The rational no having denominator $3, 7, 9, 11, 13, 17, 23, 27$.............. and multiple of these number will have non terminating decimal .
(1) $\dfrac{7}{16}$ the denominator of this rational number is not having these above number and multiple of these number, so this will have  terminating decimal.
(2) $\dfrac{23}{125}$ -- the denominator of this rational number is not having these above number and multiple of these number, so this will have  terminating decimal.
(3) $\dfrac{9}{14}$ --he denominator of this rational number is having these above number multiple of $7$, so this will have non terminating decimal.
(4)$\dfrac{32}{45}$--he denominator of this rational number is having these above number multiple of 9, so this will have non terminating decimal.
(5) $\dfrac{43}{50}$-- the denominator of this rational number is not having these above number and multiple of these number, so this will have  terminating decimal.
(6)$\dfrac{17}{40}$ -- the denominator of this rational number is not having these above number and multiple of these number, so this will have  terminating decimal.
(7)$\dfrac{61}{75}$-- he denominator of this rational number is having these above number multiple of 3, so this will have non terminating decimal.
(8)$\dfrac{123}{250}$--the denominator of this rational number is not having these above number and multiple of these number, so this will have  terminating decimal.
(i), (ii), (v), (vi) and (viii) will have  terminating decimal.

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

A rational number in its decimal expansion is $327.7081.$ What can you say about the prime factors of $q$, when this number is expressed in the form $\cfrac {p}{q}$?

  1. $q$ has prime factors $2$ or $5$ or both.
  2. $q$ has prime factors except $2$ and $5.$
  3. $q$ has no prime factors

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We know that The rational no having denominator 3, 7, 9, 11, 13, 17, 23, 27.............. and multiple of these number will have non terminating decimal .
As  decimal expansion is 327.7081 which is terminating.
prime factors of q, when this number is expressed in the form p/q will not be above number, it will be 2 or 5 or both.

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

Consider the following statements :
1. $\displaystyle \frac{1}{22}$ can not be written as terminating decimal 


2. $\displaystyle \frac{2}{15}$ can be written as a terminating decimal 

3. $\displaystyle \frac{1}{16}$ can be written as a terminating decimal 

Which of the statements given above is/are correct ?

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

$\displaystyle \frac{1}{22} = 0.04545454545$ is not a terminating decimal.

$\displaystyle \frac{2}{15}  = 0.133333333$ is not a terminating decimal.

$\displaystyle \frac{1}{16} = 0.0625$ is a terminating decimal.

Hence, statement $1$ and $3$ are correct.

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

Which one of the following is not a correct statement ?

  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. $\displaystyle 0.\overline{3}=\frac{1}{3}$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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

  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. $0.005, 0.055, 0.55, 5.5$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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

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

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

  1. Integers

  2. Whole

  3. Rational

  4. Irrational
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  1. repeats

  2. is that of a whole number

  3. has equal numerator and denominator

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

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

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

  1. has equal numerator and denominator

  2. becomes a whole number

  3. does not terminate

  4. terminates
Reveal answer Fill a bubble to check yourself
D Correct answer
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.