Terminating and Recurring decimals .pptx

Mathematics

1. Terminating and Recurring decimals Changing recurring decimals into fractions and vice versa. Grade 8

2. © T Madas A recurring decimal is a never ending decimal, whose decimal part repeats with a pattern. 0.333… 0.666… 0.1666… 0.8333… = = = = 1 3 2 3 1 6 5 6 These recurring decimals are worth remembering.

3. © T Madas A terminating decimal comes to an end after a number of decimal places. 0.25 0.4 0.52 0.3875 2.2975 1.4755859375 = = = = = = 1 4 2 5 13 25 31 80 919 400 1511 1024

4. 0.33333333… Can be written as 0. The dot shows which digit is recurring   How to change recurring decimals into fractions 0.24242424… Can be written as 0. Two digits both recur   0.714714714… Can be written as 0. The whole section between 7 and 4 recurs   0.652146521465..… Can be written as 0. The whole section between 6 and 4 recurs  

5. Change the following fractions into decimals and identify whether the answer is a recurring decimal or terminating decimal: 1) 2)   How to change fractions into recurring decimals 0 . 3 7 5 8) 3 .0 0 0 - 0 3 0 - 2 4 6 0 - 5 6 4 0 - 4 0 8x3=24 8x7=56 8x5=40 Is the same as 3÷8 Is the same as 5÷6 0 . 8 3 3….. 6) 5 .0 0 0 - 0 5 0 - 4 8 2 0 - 1 8 2 0 - 1 8 2 6x8=48 6x3=18 6x3=18 3 is a recurring =0.8   Terminating decimal Recurring decimal

6. Change 0. into a fraction   How to change recurring decimals into fractions Let X = 0.88888888…… Only one number is recurring so multiply by 10 10X = 8.888888888…… - X = 0.888888888…… 9X = 8 X =   Subtract the two Divide both sides by 9 0. =  

7. How to change recurring decimals into fractions Change 0. into a fraction   0. =   Let X = 0.7979797979…… Two numbers are recurring so multiply by 100 and 100X = 79.797979797…… - X = 0.7979797979…… 99X = 79 X =   Subtract the two Divide both sides by 99

8. Convert into a decimal Change 0. into a fraction Change the following fractions into decimals and state whether they are recurring decimals or terminating decimals ( i ) (ii) Convert into a decimal Change 0.4 into a fraction Change the following fractions into decimals and state whether they are recurring decimals or terminating decimals ( i ) (ii)   How to change recurring decimals into fractions and vice versa- Now you try…

9. Convert into a decimal Change 0. into a fraction Change the following fractions into decimals and state whether they are recurring decimals or terminating decimals ( i ) (ii) Convert into a decimal Change 0.4 into a fraction Change the following fractions into decimals and state whether they are recurring decimals or terminating decimals ( i ) (ii)   How to change recurring decimals into fractions and vice versa- Now you try… = 0.   =   = 0.15 Terminating decimal = 0.3 Recurring decimal   = 0.   =   = 0. 1 Recurring decimal   = 0.1875 Terminating decimal

10. Prove that the recurring decimal 0. =   Problem solving and reasoning Let X = 0.72727272…… Two numbers are recurring so multiply by 100 and 100X = 72.72727272…… - X = 0.7272727272…… 99X = 72 X = =   Subtract the two Divide both sides by 99 ÷ 9 ÷ 9   Simplify the fraction

11. The recurring decimal 0. can be written as the fraction Write the decimal 0. as a fraction in its simplest form   Problem solving and reasoning 0. can be written as   0. = =   + = =   0. =  

12. Reason and explain Explain why 0. is equal to 1