Question

Write the number 1.8 in the form a/b, using integers, to show that it is a rational number.

Answer 1

1.8 = 1 8/10 = 18/10 = 9/5

Answer 2

1. Note that the number 1.8 consists of two parts 1 and 0.8.

2. The decimal 0.8 can be written as the fraction $\dfrac{8}{10}.$

3. Add these two numbers:

$1+\dfrac{8}{10}=\dfrac{10}{10}+\dfrac{8}{10}=\dfrac{10+8}{10}=\dfrac{18}{10}.$

4. Since 18=2·3·3 and 10=2·5, the fraction $\dfrac{18}{10}$ can be simplified to the rational number

$\dfrac{18}{10}=\dfrac{2\cdot 3\cdot 3}{2\cdot 5}=\dfrac{3\cdot 3}{5}=\dfrac{9}{5}.$