Find whether 4 1 9 is a square or not.

Here, we have 4 1 9 . Square of a fraction is the square of its numerator and denominator. Factorise the numerator and denominator of the given fraction, we get 4 1 9 = 37 9 = 37 3 × 3 = 37 3 2 . We know that for a number to be a perfect square, all its factors should be in pair(s). Here, we get 4 1 9 = 37 3 2 . We observe that the factors of the numerator is not in pairs. So, 4 1 9 is not a square.

Find whether 4 1 9 is a square or not.

Here, we have 4 1 9 . Square of a fraction is the square of its numerator and denominator. Factorise the numerator and denominator of the given fraction, we get 4 1 9 = 37 9 = 37 3 × 3 = 37 3 2 . We know that for a number to be a perfect square, all its factors should be in pair(s). Here, we get 4 1 9 = 37 3 2 . We observe that the factors of the numerator is not in pairs. So, 4 1 9 is not a square.

Find whether 8 18 is a square or not.

Here, we have 8 18 . We get, 8 18 = 4 9 . The square of a fraction is the square of its numerator and denominator. Here, 4 9 can be expressed as 4 9 = 2 3 2 = 2 × 2 3 × 3 , 4 9 = - 2 3 2 = ( - 2 ) × - 2 3 × 3 , 4 9 = 2 - 3 2 = 2 × 2 - 3 × - 3 and 4 9 = - 2 - 3 2 = - 2 × - 2 - 3 × - 3 . We know that for a number to be a perfect square, all its factors should be in pair(s). In this case we observe that the factors of both the numerator and denominator of 8 18 = 4 9 are in pairs. Therefore, 8 18 is a square.

0 . 5 = 5 10 , right?

Here, we need to express the decimal number 0 . 5 into a fraction. We know, that while converting a decimal number into a fraction, the numerator of the fraction will be the decimal number itself without the decimal point and the denominator of the fraction will be a multiple of 10 . The number of 0 's after 1 will be equal to the number of digits in the given decimal number. Hence, while converting the decimal number 0 . 5 into a fraction, the numerator will be 5 [The decimal number 0 . 5 without the decimal point]. We observe that the number 0 . 5 has only 1 digit after the decimal point. So, the numerator will have 1 , followed by one 0 with it. Thus, the numerator will be 10 . Therefore, the fraction equivalent of the decimal number is 0 . 5 = 5 10 . This is correct. Usually, we leave the final answer in its lowest form. So, 0 . 5 = 5 10 = 5 ÷ 5 10 ÷ 5 = 1 2 . [Divide both the numerator and the denominator by the same number to reduce the fraction to its lowest term] Therefore, 0 . 5 = 5 10 = 1 2 is also correct.