Recur or Terminate

Introduction

In this lesson, you will be converting fractions to decimals using a calculator.

Type the fraction ½ on your calculator (or this if you don't have a calculator). What do you get?

This is an example of a terminating decimal. Other examples include ¾, ⅖ and ⅞.
What is a terminating decimal?

Type the fraction ⅓ on your calculator (or this if you don't have a calculator). What do you get?

This is an example of a recurring decimal. Other examples include ⅔, ⅙ and ⅚.
What is a recurring decimal?

Can you find a rule to establish whether the decimal recurs or terminates?

Hint: You may wish to use a table with the columns: "recurs", "terminates" and "don't know yet". Can you see a pattern?
Hint: what happens when there are "multiples of X"?

Further Questions and Challenges

While this activity is designed for using a calculator, it is definitely a good idea to remind yourself how to convert from a fraction to decimal by using long division. This video will remind you how! This online calculator will help check your working.

Let's take a look at the sevenths.

Convert 1/7 into a decimal (if possible by using long division)! Stop when you think there is a good reason to stop.
Now repeat for 2/7 and 3/7. What patterns have you spotted?
Without doing division, write down the decimals for 4/7, 5/7 and 6/7. Explain why.
Next, try to plot these digits of the recurring decimal on a circle (PRINT ME!). An example is on the right.
Alternatively you can do it on this virtual geoboard on nRich. Don't forget to take screenshots.
Can you see any interesting pattern/ symmetries?
Try 13 as denominator. Try with other recurring decimals.

Further Practice

Take this opportunity to brush up on your skills converting between fractions and decimals. You may also wish to practise the four operations on fraction, decimal and percentages. Do the relevant skills practice on DrFrostMaths, CorbettMaths, MyiMaths and Eedi. Watch any video and/or go through any online lesson as you see fit.

Transum

Recurring Decimals: Change recurring decimals into their corresponding fractions and vica versa.
Fraction Decimal Pairs: The traditional pairs or Pelmanism game adapted to test knowledge of simple fractions and their equivalent decimals.
Fraction Percentage Pairs: The traditional pairs or Pelmanism game adapted to test knowledge of simple fractions and their equivalent percentages.
Fraction Percentage: Match the fraction with the equivalent percentage. A drag and drop self marking exercise.
Fractions, Decimals, Percentages: An exercise on converting fractions to decimals, decimals to percentages and percentages to fractions.
Particular Pipes: Construct the pipes using a set number of pieces with lengths given as fractions, decimals or percentages.

For more goodies on Fractions, Decimals and Percentages on Transum, click on the hyperlinks.

Extension

Here's an example of how to calculate ALL the answers quickly using a spreadsheet

Here are some excellent nRich tasks on the topic of fractions:

Finally, try the task on the right!

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