Question

Heya!!

Which of the following will have a terminating decimal expansion?

$a) \frac{77}{210}$

$b) \frac{47}{50}$

$c) \frac{28}{132}$

$d) \frac{23}{8}$
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Answer 1

$\mathfrak{Answer:}$

= Option b and d.

$\mathfrak{Step-by-Step\:Explanation:}$

Terminating Decimal :

• If after a finite numbers of steps in the division process , when there is nothing as remainder.
• A fraction p/q is a terminating decimal if its prime factors of q are 2 or 5.

$\bold{a.\quad \dfrac{77}{210}}\\\\\\\tt{q=210=2\times 3\times 5\times 7}\\\\\\\textsf{It contains 3 and 7 also.}\\\\\\\tt{So\:option(a)\quad\boxed{X}}\\\\\\\\\bold{b.\quad \dfrac{47}{50}}\\\\\\\tt{q=50=2\times 5\times 5}\\\\\\\textsf{So it can be expressed in a terminating decimal.}\\\\\\\bold{c.\quad\dfrac{28}{132}}\\\\\\\tt{q=132=2\times2\times3\times11}\\\\\\\textsf{It also contains 3 and 11.}\\\\\\\tt{So\:option(c)\quad\boxed{X}}\\\\\\\bold{d.\quad\dfrac{23}{8}}$

$\tt{q=8=2\times 2\times2}\\\\\\\textsf{So it can be expressed in a terminating decimal.}$

Answer 2

$\huge\boxed{\texttt{\fcolorbox{purple}{pink}{Heya !!!}}}$

A TERMINATING DECIMAL EXPANSUON MEANS THE NUMBERS AFTER DECIMAL POINT DOES NOT CONTINUE.

WE CHECK WHETHER A FRACTION IS TERMINATING OR NOT BY DIVIDING.

THE DIVISION IS SHOWN IN THE PICTURE.

PLEASE REFER THE PICTURE.

ACCORDINGLY,

OPTION B AND D ARE TERMINATING DECIMAL EXPANSION.




FOR MORE INFORMATION....

A DECIMAL EXPANSION CAN BE EITHER TERMINATING OR NON-TERMINATING.

TERMINATING DECIMAL EXPANSION ARE RATIONAL NUMBERS.

NON-TERMINATING DECIMAL EXPANSION CAN EITHER BE OF RECCURING THAT MEANS REPEATING OR NOB-RECCURING THAT MEANS NON-REPEATING.

NON-TERMINATING RECCURING DECIMAL EXPANSION IS RATIONAL NUMBER.

WHILE NON-TERMINATING NON-RECCURING DECIMAL EXPANSION IS IRRATIONAL NUMBER.

NOW,NON-TERMINATING RECCURING DECIMAL EXPANSION CAN EITHER BE AS IN A SINGLE DIGIT REPEATING OR A BUNCH OF NUMBERS REPEATING.

A BAR CAN BE USED ON THE NUMBER WHICH ARE REPEATING IN A DECIMAL EXPANSION.

HOPE IT HELPS YOU❤❤❤