Question

Which of the following statements is correct if the numbers are arranged from the smallest to the largest?

• A. $\frac{22}{7},3.14,\mathrm{3.141141114...},3.\overline{14}$
• B. $3.14,\mathrm{3.141141114...},3.\overline{14},\frac{22}{7}$
• C. $3.\overline{14},\frac{22}{7},\mathrm{3.141141114...},3.14$
• D. $\mathrm{3.141141114...},\frac{22}{7},3.14,3.\overline{14}$

Answer 1

The correct option is B $3.14,\mathrm{3.141141114...},3.\overline{14},\frac{22}{7}$

Detailed step-by-step solution:
$\frac{22}{7}-3.\overline{142857}=\mathrm{3.142857142857...}$
$3.\overline{14}=\mathrm{3.14141414...}$
$3.14=3.1400$
$\mathrm{3.141141114...}=\mathrm{3.141141114...}$

Let us consider the first four digits after the decimal point of all the numbers.
Based on this, we can arrange it from the smallest to the largest.
Accordingly, the four numbers can be written as $3.1428,3.1414,3.1400,$ and $\mathrm{3.1411.}$

$3.1400<3.1411<3.14114<3.1428$
$\Rightarrow 3.14<\mathrm{3.141141114...}<3.\overline{14}<\frac{22}{7}$

So, option D is the correct answer.