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

$\dfrac {1}{2} = 0.5$
It is a terminating decimal because the denominator has a factor as ...........

  1. $0$
  2. $1$
  3. $2$
  4. $6$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If the prime factors in the denominator of a fraction has factors of $2$ and $5$, then the decimals terminate. The denominator has $2$ as a factor.
Therefore, $C$ is the correct answer.

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

When the division process does not end and the remainder is not equal to zero; then such decimal is known as ............... decimal

  1. terminating

  2. non-terminating

  3. recurring

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

The division is completed when we get the remainder zero. In this division process we do not get a zero and it is never ending. This process of division is called a non- terminating decimal.
Therefore, $B$ is the correct answer.

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

Which of the following fractions will terminate when expressed as a decimal? (Choose all that apply.)

  1. $\frac{1}{256}$
  2. $\frac{27}{100}$
  3. $\frac{100}{27}$
  4. $\frac{231}{660}$
  5. $\frac{7}{105}$
Reveal answer Fill a bubble to check yourself
A,B,D Correct answer
Explanation

Recall that in order for the decimal version of a fraction to terminate, the fraction's denominator in fully reduced form must have a prime factorization that consists of only 2's and/or 5's. 

The denominator in (A) is composed of only 2's $(256 = 2^8)$. 
The denominator in (B) is composed of only 2's and 5's $(100=2^2\times 5^2)$. 
In fully reduced form, the fraction in (D) is equal to $\frac{7}{20}$ and 20 is composed of only 2's and 5's $(20=2^2\times 5)$.
 By contrast, the denominator in (C) has prime factors other than Z's and 5's $(27 =3^3)$, and in fully reduced form, the fraction in (E) is equal to $\frac{1}{15}$, and 15 has a prime factor other than 2's and 5's $(15 = 3 \times 5)$.

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

Identify a non-terminating repeating decimal.

  1. $\dfrac{24}{1600}$
  2. $\dfrac{171}{800}$
  3. $\dfrac{123}{2^2 \times 5^3}$
  4. $\dfrac{145}{2^3 \times 5^2 \times 7^2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
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

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

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

  1. $2$ or $5$
  2. $2$, $3$ or $5$
  3. $3$ or $5$
  4. Only $2$ and $3$
Reveal answer Fill a bubble to check yourself
A Correct answer
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

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

Which one of the following has a terminating decimal expansion?

  1. $\displaystyle\frac{5}{32}$
  2. $\displaystyle\frac{7}{9}$
  3. $\displaystyle\frac{8}{15}$
  4. $\displaystyle\frac{1}{12}$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

Which of the following numbers has the terminal decimal representation?

  1. $\dfrac{1}{7}$
  2. $\dfrac{1}{3}$
  3. $\dfrac{3}{5}$
  4. $\dfrac{17}{3}$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.
Multiple choice maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

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 _________.

  1. Terminating decimal

  2. Non-terminating decimal

  3. Non-terminating and non-repeating decimal

  4. Terminating repeating decimal
Reveal answer Fill a bubble to check yourself
A Correct answer
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