Question

The numbers 3.444... and 3.555 ... are both irrational numbers. Which of the following is a rational number?a) 4.445444....b) 3.445444...c) 3.445d) 3.554555....

Answer 1

c) 3.445

Step-by-step explanation

It is important to first know what a rational number is.

A rational number is one that can be represented as a fraction of two integers:

`\begin{gathered} (a)/(b) \\ \text{where a, b = integer} \end{gathered}`

Therefore, 3.444... and 3.555... are irrational because they cannot be represented as simple fractions of two integers.

They are non-terminating decimals. They do not end.

From the options given, we see that only one option is a terminating decimal unlike the others.

That is 3.445.

It can be written as a fraction of two integers:

`\begin{gathered} (3445)/(1000) \\ It\text{ can be reduced to } \\ (689)/(200) \end{gathered}`

As we can see, 3.445 is a rational number.