rafe
Uploaded by
13 SLIDES
332 VUES
140LIKES

Understanding Terminating and Repeating Decimals: Conversion and Examples

DESCRIPTION

This project explores the concepts of terminating and repeating decimals, focusing on how to convert fractions into decimal form and vice versa. Terminating decimals are finite decimal numbers, while repeating decimals continue indefinitely with a recurring sequence. We provide examples of both types, along with clear guidelines for identifying the nature of a decimal based on its denominator. The project also includes simple methods to convert terminating decimals into fractions and a step-by-step approach for transforming repeating decimals into fractional form.

1 / 13

Télécharger la présentation

Understanding Terminating and Repeating Decimals: Conversion and Examples

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Calculus Project 1.2 By Dorothy McCammon, Tammy Boals, George Reeves, Robert Stevens

  2. Part 1 • When you have a fraction x/y, y can be divided into x to obtain that fraction in decimal form. • There are two different types of decimal numbers you can obtain.

  3. Terminating decimals are decimals that don’t continue infinitely. Terminating Decimal

  4. Examples of Terminating Decimals 1/2 = .5; 1/5 = .2; 1/10 = .1 1/4 = .25; 1/25 = .04; 1/125 = .008 1/625 = .0016; 1/2500 = .0004 Note that all of these values end; they don’t continue with a repeating decimal value.

  5. Repeating Decimal • Repeating decimals are decimal values that never end; they just continue to repeat the same values.

  6. Examples of Repeating Decimals 1/3 = .3333~ 1/6 = .16666~ 1/9 = .1111~ 1/11 = .0909~ 1/33 = .0303~ 1/99 = .010101~ Note that these values are never-ending. They will continue to repeat.

  7. How can one tell which type of decimal they’ll get? • It’s very simple. As long as the denominator is made of the numbers (2^x)(5^y) where x and y are nonnegative integers, the value will be terminating.

  8. 1/(2^3)(5^4) = .0002 1/(2^5)(5^6) = .000002 1/(2^2)(5^3) = .002 All of these values are terminating. Examples

  9. Decimal to fraction Part 2 • If you are given a decimal instead of a fraction, how can you make it a fraction when it is either terminating or repeating?

  10. Terminating into a fraction • Terminating decimals are easy to turn into fractions. You can just put the value over 10,100,1000, etc; the denominator depends on the decimal place.

  11. Examples • .1 = 1/10 .01 = 1/100 .001 = 1/1000 .0001 = 1/10000 .5 = 5/10 = 1/2 .25 = 25/100 = 1/4 These values are easy to convert. Making the new fraction is very simple.

  12. Repeating into fraction • Converting repeating decimals is a bit more complicated. Let’s take 3.135135 for example. We can set it equal to r: r = 3.135135 There are 3 repeating values so we will set it equal to 1000r = 3135.135135

  13. Next we do 1000r – r = 3135.135135 note that r = 3.135135 We now have 999r = 3132 so r = 3132/999 = 226/37

More Related