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 $1.01,\dfrac{21}{19},1.011111...$

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.

$\dfrac{21}{19}=1.10526315789$

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, $1.10526315789=\dfrac{21}{19}$ 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

$1.01,1.011111...,\dfrac{21}{19}$

Therefore, the correct option is C.