Welcome to Clip from Spiral logo

Interactive video lesson plan for: Converting a Repeating Decimal to a Fraction

Activity overview:

Save time with this short cut method for converting a repeating decimal to a fraction. It even works on a crazy repeating decimal like,
.706438898889

Transcript
Welcome to MooMooMath where we upload a new Math video everyday. In this video I would like to show a shortcut for converting repeating decimals to a fraction.
First the rules.
First, with the numerator, if you only have repeating numbers like .222 you write the repeating number as your numerator.
If you have a mixed recurring decimal like .16666 subtract
Notice the 1 does not repeat like the 6.
The non-repeating number from the repeating number. Make sure the repeating number has the same number of digits as the repeating number.
The denominator rules for non-repeating numbers, add a 0 ,and a 9 for repeating numbers.
Once you write the fraction you then reduce.
Lets work a couple of examples.
Lets start with .333 which is a repeating digit without any non-repeating numbers.
I will write 3 as the numerator, and nine for the repeating number.
I can reduce this down to 1/3
Another example .666
Write 6 which is the repeating number, you have one repeating number so write a nine.
This will reduce to 2/3
Lets go with .833 which has a non-repeating number.
What we will do is subtract the repeating number 83 minus 8 because that is the non-repeating number.
83-8 equals 75, which becomes your numerator.
We have 1 non-repeating number so I will write a 0 and a 9 for the repeating number. 75/90 reduces to 5/6
How about this example?
.1818 we have a repeating number with two digits so I will write 18 and then for the denominator I will write a 9 for each digit which becomes 99 and 18 over 99 can be reduced to 2/11
Lets work a couple more.
.16 we have a non-repeating number.
I will take the repeating number minus the non-repeating number which is 1 and subtract which equals 15
15 over 0 for the non-repeating number and a 9 for the repeating number which becomes 15 over 90 and you can reduce to 1/6
I took 16 minus 1 which is your non-recurring which equals 15 over 90 which reduces to 1/6
The one exception I have found is this,
Take .4166 and you may write the repeating number as 416 but because you have two non-repeating numbers you need at least two repeating numbers. Instead of writing 416 write 4166. From there is would be 4166 minus 41 equals 4125 and 4125 over two non-repeating and two repeating and I cheated and put this in a fraction reduce, which reduces to 5/12
Let me go through two more just to show how this works.
Take .251818 repeating.
Take the repeating fraction of .2518 minus the non-repeating and you have two non-repeating minus 25 because that is the non-repeating portion.
2518 - 25 equals 2493 and you have two non-repeating so write 00 and two repeating numbers so write 99 and simplify to 277/1100 and if you divide it equals .2518
I will show you a crazy number like .70643889889
The repeating is 889 you can see it repeating twice.
I will first write the repeating decimal 70643889 minus the non-repeating of 70643 and when you subtract you get 70573246 and I will write it again 70573246 and use the same rules for the denominator.
For the non-repeating I add a 0 and I have 1 2 3 4 5 zeros.
1 2 3 4 5 and three repeating numbers and three non-repeating 999 and that is your fraction I will not reduce, but test it out and if you divide the numbers it will equal the repeating fraction. It does work
Hope this helps with converting repeating decimals to a fraction
MooMooMath uploads a new Math video everyday.

-~-~~-~~~-~~-~-
Please watch: "Study Skills Teacher's Secret Guide to your Best Grades"
https://www.youtube.com/watch?v=f3bsg8gaSbw
-~-~~-~~~-~~-~-
Learn even more about fractions with this fraction playlist that covers the basics of fractions!!
https://www.youtube.com/playlist?list=PLurjkZV1ykGa0cb4iAUs2FZLS-ClkRHmq

Tagged under: repeating decimal,recurring decimal,repeating decimal fraction,changing repeating decimal fraction,numbers,decimals,decimals fraction,shortcut,moomoomath

Clip makes it super easy to turn any public video into a formative assessment activity in your classroom.

Add multiple choice quizzes, questions and browse hundreds of approved, video lesson ideas for Clip

Make YouTube one of your teaching aids - Works perfectly with lesson micro-teaching plans

Play this activity

1. Students enter a simple code

2. You play the video

3. The students comment

4. You review and reflect

* Whiteboard required for teacher-paced activities

Share on:

Share Converting a Repeating Decimal to a Fraction on Google+ Share Converting a Repeating Decimal to a Fraction on Twitter Share Converting a Repeating Decimal to a Fraction on Facebook Pin Converting a Repeating Decimal to a Fraction Email Converting a Repeating Decimal to a Fraction

Ready to see what else Spiral logo can do?

With four apps, each designed around existing classroom activities, Spiral gives you the power to do formative assessment with anything you teach.

Quickfire

Carry out a quickfire formative assessment to see what the whole class is thinking

Discuss

Create interactive presentations to spark creativity in class

Team Up

Student teams can create and share collaborative presentations from linked devices

Clip

Turn any public video into a live chat with questions and quizzes

1000s of teachers use Spiral to deliver awesome, engaging activities that capture students' understanding during lessons.

Now it's your turn Sign up

Spiral Reviews by Teachers and Digital Learning Coaches

Spiral
Review of Spiral by teacher: Kathryn Laster @kklaster

Tried out the canvas response option on @SpiralEducation & it's so awesome! Add text or drawings AND annotate an image! #R10tech

Spiral
Review of Spiral by teacher: Room 220 Math Stars @3rdgradeBCE

Using @SpiralEducation in class for math review. Student approved! Thumbs up! Thanks.

Spiral
Review of Spiral by teacher: Miss Ord @ordmiss

Absolutely amazing collaboration from year 10 today. 100% engagement and constant smiles from all #lovetsla #spiral

Spiral
Review of Spiral by teacher: Adam J. Stryker @strykerstennis

Students show better Interpersonal Writing skills than Speaking via @SpiralEducation Great #data #langchat folks!

Spiral
Review of Spiral by teacher: Dr Ayla Göl @iladylayla

A good tool for supporting active #learning.

Spiral
Review of Spiral by teacher: Brett Erenberg @BrettErenberg

The Team Up app is unlike anything I have ever seen. You left NOTHING out! So impressed!

Get the Clip Chrome Extension & Create Video Lessons in Seconds

Add Clip to Chrome