Question

Is 3/24.represents terminating decimal?
Give reason and find its decimal form

Answer 1

Answer:

• Yes , 3/24 represents terminating decimal expansion ( terminating after 3 digits of decimal)

• Reason : The denominator of its simplest form can be written in the form 2^m × 5^n .

• 3/24 = 0.625

Note:

★ Rational number : A number in the form of p/q where p and q are integers and q≠0 is called rational number.

★ Rational numbers are characterized as follow ;

1) Terminating

2) Non-terminating but repeating

( Non-terminating but recurring )

★ The rational number p/q in its simplest form is said to be terminating if its denominator q can be written in the form of 2^m × 5^n (it will terminates after m digits of decimal ) , otherwise it is said to be Non-terminating but repeating .

★ Irrational number : The numbers which are not rational number are called Irrational numbers. Such numbers can't be written in the form of p/q where p and q are integers and q ≠ 0 .

★ Irrational numbers are characterized as Non-terminating Non-repeating

( or Non-terminating Non-recurring )

Solution:

Here,

The given rational number is 3/24 .

The simplest form of the given rational number 3/24 is : 1/8

Now ,

The denominator of the given rational number in simplest form (ie ; 8) can be written as ;

8 = 2^3

8 = 2^3 × 5^0

Clearly,

The denominator is of the form 2^m × 3^n .

Thus,

The given rational number is terminating .

Moreover,

It will terminates after 3 digits of decimal .

Now,

=> 3/24 = 1/8

1

=> 3/24 = ---------------

2 × 2 × 2

5 × 5 × 5

=> 3/24 = -------------------------------

(2×5) × (2×5) × (2×5)

5 × 5 × 5

=> 3/24 = -------------------

10 × 10 × 10

=> 3/24 = 625 / 1000

=> 3/24 = 0.625

Hence,

The given rational number 3/24 is terminating (terminates after 3 digits of decimal) and can be written decimal number 0.625 .