Tag: real number

Questions Related to real number

Multiple choice maths real number real numbers on number line fundamental theorem of arithmetic common factors and hcf

Three ropes are $7\ m, 12\ m\ 95\ cm$ and $3\ m\ 85\ cm$ long. What is the greatest possible length that can be used to measure these ropes?

  1. $35\ cm$
  2. $55\ cm$
  3. $1\ m$
  4. $65\ cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The given three ropes are $7$m, $12$ m $95$cm and $3$m$85$cm long. We know that $1$m=$100$cm, therefore,


The length of the respective ropes will be:

1st rope $=7\times 100=700$cm
2nd rope $=(12\times 100)+95=1200+95=1295$cm
3rd rope $=(3\times 100)+85=300+85=385$cm

Now, let us factorize the length of the ropes as follows:

$700=2\times 2\times 5\times 5\times 7\ 1295=5\times 7\times 37\ 385=5\times 7\times 11$

The highest common factor (HCF) is $5\times 7=35$

Hence, the greatest possible length that can be used to measure these ropes is $35$cm.

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.