Question

find two rational number of the form P by Q between the numbers 0.2121121112111.... and 0.20200200020000....

Answer 1

Add the two numbers:

0.2121121112 0.2020020002 -------------- 0.4141141114

Then divide by two to get the average:

0.2070520552 (deliberate mistakes)

Here’s how to finish that average:

Find my mistakes, correct themWrite the decimal as a fraction (ten-billionths)Simplify the fraction(divide numerator and denominator by common factor)

However, some people might want to use Calculator Tricks to find random rational and irrational numbers between two numbers.

The left image shows my INPUT into the program to generate numbers between A and B. The second image shows four rational numbers and four irrational numbers between .2121121112 and .2020020002.

To convert the rational numbers into fractions, just read these fractions in “English” and then write them as a fraction. For example:

0.210734752 = 210734752 billionths = 210734752" role="presentation" style="margin: 0px; padding: 0px; outline: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">2107347521000000000210734752Don’t forget to simplify the fractions.

Answer 2

Answer:

First rational number : 0.2071

Second rational number : 0.2096

Step-by-step explanation:

To find rational number (r) between two numbers m and n :

$r = \frac{m+n}{2}$

Let m = 0.212112111..... and n = 0.2020020000.....

First rational number,

$r_1=\frac{0.212112111... + 0.202002000....}{2}\\\\\implies r_1=0.2071$

Second rational number,

$r_2=\frac{0.212112111... + 0.2071}{2}\\\\\implies r_2=0.2096$

Hence, we are able to find two rational numbers between the given two numbers.

First rational number : 0.2071

Second rational number : 0.2096