Tag: rational numbers as recurring/terminating decimals

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

If a number has a non-terminating and non-recurring decimal expansion, then it is.

  1. A rational number

  2. A natural number

  3. An irrational number

  4. An integer
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A number having non-terminating and non-recurring decimal expansion is an Irrational Number


for example 

$\pi$  is an irrational number 

$\pi = 3.1415926535897932384626433832............$


the number has non-terminating decimal expansion and non-recurring.

So option $C $ is correct

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

State the following statement is True or False

$\dfrac {15}{1600}$ has a terminating decimal expansion .

  1. True

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

Given, $\displaystyle \frac {15}{1600}= \frac {15}{5^{2}2^{6}}$
As it is in the form of ${ 2 }^{ m }\times { 5 }^{ n }$ where ($n=6,m=2$).
So, the rational number $\displaystyle \frac {15}{1600}$ has a terminating decimal expansion

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 numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
$\dfrac {29}{343}$

  1. Terminating

  2. Non-terminating

  3. Ambiguous

  4. Data insufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given, $\displaystyle \frac {29}{343}= \frac {29}{7^{3}}$
As it is not in the form of ${ 2 }^{ m }\times { 5 }^{ n }$.
So, the rational number $\displaystyle \frac {29}{343}$ has a non terminating decimal expansion

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

Convert the following fraction into simple decimal recurring form.

$\displaystyle \frac{1}{6}$= ?

  1. $0.1\bar 9$
  2. $0.1\bar 6$
  3. $0.1\bar 4$
  4. $0.1\bar 3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
    Pure recurring decimal is a decimal fraction in which all the figures after the decimal point are repeated.
    $\displaystyle \frac { 1 }{ 6 }= 0.6666666666..$ is $ 0.\overset { \ _ \ _  }{ 6 } $.
Multiple choice maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

Find whether it is a terminating or a non-terminating decimal.

$2.4 \div 0.072$.

  1. Terminating

  2. Non-terminating

  3. Ambiguous

  4. Data insufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A terminating decimal is a decimal that ends. It's a decimal with a finite number of digits.

$2.4\div 0.072=33.3333333333....$.
The division gives recurring factor.
Hence, it is a non-terminating decimal.