Given:
The list of numbers have three numbers [tex]1.01,\dfrac{21}{19},1.011111...[/tex]
To find:
The correct list which shows numbers ordered least to greatest.
Solution:
First we have to convert all numbers in decimal form.
Here, two numbers are already in decimal form.
[tex]\dfrac{21}{19}=1.10526315789 [/tex]
All numbers before decimal are equal, i.e., 1. So, check the numbers after decimal.
Two numbers [tex]1.01,1.011111...[/tex] have 0 after decimal and [tex]1.10526315789 [/tex] has 1 after decimal. So, [tex]1.10526315789=\dfrac{21}{19} [/tex] number is greatest.
Now, compare the digit on hundredth place (second place after decimal).
Both numbers 1.01 and1.011111... have 1 on hundredth place.
Now, compare the digit on thousandth place (third place after decimal).
Number 1.01 have nothing on thousandth place. So, it is 0.
Number 1.011111... has 1 on thousandth place. So, 1.011111... is greater than 1.01.
Now, the arrangement in ordered least to greatest is
[tex]1.01,1.011111...,\dfrac{21}{19}[/tex]
Therefore, the correct option is C.
