Question

Without actual division state the type of decimal expansion no 7/75

Answer 1

Answer:

Non-terminating but repeating

Note:

• Rational number - A number which can be written in the form of p/q where p and q are integers but q≠0 are called rational number.

• Rational number are characterized as:

1) Terminating

2) Non-terminating but repeating

(or Non-terminating but recurring)

• A Rational number p/q (in its simplest form) is said to be terminating if its denominator q can be written as ; 2^m × 5^n (otherwise it is called Non-terminating but repeating).

Solution:

The given Rational number is : 7/75

Clearly,

The given Rational number 7/75 is in simplest form.

Also,

The denominator of the rational number 7/75 can be written as ; 75 = 3 × 5²

Clearly,

The denominator of 7/75 (ie; 75) is not of the form 2^m × 5^n , thus 7/75 is Non-terminating but repeating.

Hence,

7/75 has non-terminating repeating decimal expansion.