Question

Explain why 3.1416 is a rational number

Answer 1

3.1416 is a rational number because it can be written as $\dfrac{p}{q}$ form.

Step-by-step explanation:

We have,

3.1416

To explain 3.1416 is a rational number, why ?

∴ 3.1416

Multiplying and dividing by 10000, we get

= $\dfrac{3.1416\times 10000}{10000}$

= $\dfrac{31416}{10000}$

The HCF of 31416 and 10000 = 8

Dividing numerator and denominator by 8, we get

= $\dfrac{\dfrac{31416}{8}}{\dfrac{10000}{8}}$

= $\dfrac{3927}{1250}$

The rational number is defined as "it can be written as $\dfrac{p}{q}$ form, where q ≠ 0.

= $\dfrac{3927}{1250}$, is a form of $\dfrac{p}{q}$, it is a rational number.

Thus, 3.1416 is a rational number because it can be written as $\dfrac{p}{q}$ form.