Question

Write the rational number 2.25in non terminating reccuring decimal form​

Answer 1

Answer:

If p/q is a fraction.

Then the condition to find whether the decimal representation of this fraction gives terminating decimal or non terminating recurring we will be taking help of denominator.

If prime factorization of denominator contains only 2’s & 5’s or 2’s or 5’s then fraction will give terminating decimal.

For example 7/5 = 1.4,

9/2 = 4.5,

7/25 = .28,

9/4 = 2.25 etc.

If prime factorization of denominator contains other numbers also a 3,7,9,11 etc, then decimal representation will give non terminating recurring decimal.

For example 7/6=1.1666.,

11/9=1.2222..,

23/7=3.285714255714…. etc.