Question

Which list shows numbers ordered least to greatest? A. 1.01, 21/19, 1.01 repeated B. 21/19, 1.01, 1.01 repeated C. 1.01, 1.01 repeated, 21/19 D. 1.01 repeated, 1.01, 21/19

Answer 1

Given:

The list of numbers have three numbers
`1.01,(21)/(19),1.011111...`

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.

`(21)/(19)=1.10526315789`

All numbers before decimal are equal, i.e., 1. So, check the numbers after decimal.

Two numbers
`1.01,1.011111...` have 0 after decimal and
`1.10526315789` has 1 after decimal. So,
`1.10526315789=(21)/(19)` 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

`1.01,1.011111...,(21)/(19)`

Therefore, the correct option is C.