Look at the decimal 0.121122111222... If the pattern continues, is this a repeating decimal?
asked Aug 27, 2014 in Other Math Topics by anonymous

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

3 Answers

NO it DONT repeet...number av "2" vary
answered Aug 27, 2014 by muneepenee
is 0.121122111222... a repeating decimal if it kepps going
answered 6 days ago by anonymous

This is not a recurring decimal even though it is a repeating pattern.

This decimal can be represented by the sum of two series. First write the number as 0.10110011100011110000... + 0.0200220002220000...

We can write this sum as:

(⅟₉)(0.9099009990009999... + 2×(0.090099000999...)).

We can write this as:

(⅟₉)∑[(10ⁿ-1)/10^n²)(1+2/10ⁿ)] where ∑ means “sum of” and is applied to the terms in the square brackets where n is an integer greater than 0.

From this we can see that the nth term is expressed by the quantity in the square brackets. To see this more clearly put n=1 to give us the first term:

(⅟₉)(10-1)/10)(1.2)=0.12=3/25.

Now, n=2:

(⅟₉)(100-1)/10000)(1.02)=0.001122=561/500000;

and n=3:

(⅟₉)(1000-1)/10⁹)(1.002)=0.000000111222=55611/(5×10¹¹).

Add these together: 0.121122111222, a finite decimal.

A recurring decimal always represents one unique fraction, but it’s clear that the fraction given by the formula produces a finite decimal (with n²+n decimal places) and a changing fraction as n increases. Therefore, the given decimal cannot be a repeating (recurring) decimal and it has an infinite number of decimal places as n➝∞.

answered 5 days ago by Rod Top Rated User (559,680 points)

Related questions

Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
81,275 questions
85,406 answers
2,164 comments
68,895 users