20 Jun ##0.0bar(9) = 1/10## or ##0.bar(09) = 1/11## We will be usin
##0.0bar(9) = 1/10## or ##0.bar(09) = 1/11## We will be using the notation that ##0.099999… = 0.0bar(9)## This avoids any ambiguity as to which digits are repeating. There are lots of ways to show that ##0.bar(9) = 1##. Once we have that then we simply divide by sides by 10 and we are done. ##0.0bar(9) = 1/10*0.bar(9) = 1/10*1 = 1/10## . . . Now in this case we used our prior knowledge that ##0.bar(9)=1## to show what we wanted however what if there is a different repeating decimal? For example how would we find the fraction representation of ##0.bar(21)##? Here’s one way: Let ##x = 0.bar(21)## Then multiply each side by ##100## (note that this is because there are ##2## digits in ##21## and ##100 = 10^2##). ##100x = 21.bar(21)## Note that despite shifting the decimal two places because there were infinite ##21##s after the decimal originally there are still infinite ##21##s after the decimal. Now subtract ##x## from both sides noting that ##x = 0.bar(21)## ##100x – x = 21.bar(21) – 0.bar(21)## ##=> 99x = 21## ##=> x = 21/99 = 7/33## This trick will work for any repeating decimal so long as you multiply by ##10^k## where ##k## is the number of digits that repeat. The idea is to shift the decimal without changing the value afterwards thereby allowing the subtraction trick shown above. This trick incidentally is one of the methods shown in the above link demonstrating that ##0.bar(9) = 1##. As a final note if the initial question was referring to ##0.bar(09)## and not ##0.0bar(9)## then applying the same trick we have ##x = 0.bar(09)## ##=> 100x = 9.bar(09)## ##=> 100x – x = 9.bar(09) – 0.bar(09)## ##=> 99x = 9## ##=> x = 9/99 = 1/11##
Our website has a team of professional writers who can help you write any of your homework. They will write your papers from scratch. We also have a team of editors just to make sure all papers are of HIGH QUALITY & PLAGIARISM FREE. To make an Order you only need to click Ask A Question and we will direct you to our Order Page at WriteDemy. Then fill Our Order Form with all your assignment instructions. Select your deadline and pay for your paper. You will get it few hours before your set deadline.
Fill in all the assignment paper details that are required in the order form with the standard information being the page count, deadline, academic level and type of paper. It is advisable to have this information at hand so that you can quickly fill in the necessary information needed in the form for the essay writer to be immediately assigned to your writing project. Make payment for the custom essay order to enable us to assign a suitable writer to your order. Payments are made through Paypal on a secured billing page. Finally, sit back and relax.
About Writedemy
We are a professional paper writing website. If you have searched a question and bumped into our website just know you are in the right place to get help in your coursework. We offer HIGH QUALITY & PLAGIARISM FREE Papers.
How It Works
To make an Order you only need to click on “Order Now” and we will direct you to our Order Page. Fill Our Order Form with all your assignment instructions. Select your deadline and pay for your paper. You will get it few hours before your set deadline.
Are there Discounts?
All new clients are eligible for 20% off in their first Order. Our payment method is safe and secure.