Tag: real number

Quizzes (6) Questions (132)

Questions Related to real number

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 fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic


$20$ is written as the product of primes as :

  1. ${2\times 5 }$
  2. ${2\times 2\times 3\times 5}$
  3. ${2\times 2\times 5}$
  4. ${2\times 2\times 3}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To write a number as product of its primes, we divide it by various prime numbers $ 2, 3, 5, 7 $ etc one by one and check by which prime numbers it is divisible with and how many times.

Hence, $ 20 = 2 \times 10 = 2 \times 2 \times 5 $