Question

Evaluate the following and express the answer as a rational number in its standard form.

1.3 × 1.03 (in 1.03, 03 is reccuring)

Answer 1

Answer:

Step I: Obtain the rational number.

Step II: See whether the denominator of the rational number is positive or not. If it is negative, multiply or divide numerator and denominator both by -1 so that denominator becomes positive.

Step III: Find the greatest common divisor (GCD) of the absolute values of the numerator and the denominator.

Step IV: Divide the numerator and denominator of the given rational number by the GCD (HCF) obtained in step III. The rational number so obtained is the standard form of the given rational number.

The following examples will illustrate the above procedure to convert a rational number into standard form.

1. Express each of the following rational numbers in the standard form:

(i) \(\frac{-9}{24}\) (ii) \(\frac{-14}{-35}\) (iii) \(\frac{27}{-72}\) (iv) \(\frac{-55}{-99}\)−924 (ii) −14−35 (iii) 27−72 (iv) −55−99

Solution:

(i) \(\frac{-9}{24}\)−924

The denominator of the rational number \(\frac{-9}{24}\) is positive. In order to express it in standard form, we divide its numerator and denominator by the greatest common divisor of 9 and 24 is 3. −924 is positive. In order to express it in standard form, we divide its numerator and denominator by the greatest common divisor of 9 and 24 is 3.

Dividing the numerator and denominator of −924 by 3, we get

−924 = (−9)÷324÷3 = −38

Thus, the standard form of −924 is −38.