1. Recurring Decimal Fraction  Recurring Decimal
Representing Recurring Decimal
Recurring Decimal  Fraction

2. Fraction  Recurring Decimal
43/10 = 4.3 5/8 = /25 = /3 = ?
10 = 2 x 5 8 = 2 x 2 x 2 25 = 5 x 5

3. Fraction  Recurring Decimal 1
7/3 = 2 . 3 3 …

4. Fraction  Recurring Decimal 2. 3 6 3 …
4/11 =

5. Recurring Decimals 2.33333… = 2 + 0.333333… 2.81515… = 2 + 0.8151515…
So enough to look at recurring decimals < 1
Or recurring decimal = 0.*****….
Where * = any number (e.g. 3 or 15)

6. Representing Recurring Decimal 1
How many windows in the engine?
How many windows in the compartment? =
 … = 3 4 5 2 6 2
No. of engine-windows = 2
No. of compartment-windows = 3 . 3 0. 26
345 .

7. Representing Recurring Decimal 2
No. of engine-windows = 1 …
 … = 0.94
No. of compartment-windows = 1
= … 9 4 4 …
= 0.94 ˙ ˙

8. Representing Recurring Decimal 3
No. of engine-windows = 1 …
 … = 0.815
 … = 2.815
No. of compartment-windows = 2
= … 8 1 5 1 5 …
= 0.815 ˙ ˙ ˙

9. Representing Recurring Decimal 4
No. of engine-windows = 2 …
 … =
No. of compartment-windows = 2
= … 6 2 3 7 3 7 … = ˙ ˙

10. Representing Recurring Decimal 5
No. of engine-windows = …
 … = 0.923
No. of compartment-windows = 3
= … 2 3 9 … 2 3 9
= 0.923 ˙
There is no engine like previous examples, imagine a small one as in local trains  ˙

11. Representing Recurring Decimal 6
No. of engine-windows = 2 …
 … =
No. of compartment-windows = 2
= … 7 3 3 … = ˙ ˙

12. Representing Recurring Decimal9 4 … 1 5 8 … 6 2 3 7 … 7 3 … 2 3 9 … 3 4 5 2 6 …
= 0.94 ˙ … … … … …
= 0.815 ˙ = ˙
= 0.923 ˙ = ˙ = ˙

13. Recurring Decimal  Fraction 13 4 5 2 6 … ˙
… = x 1
… = x
… = x ˙ 10 ˙
100
Now the engine is before the decimal point.
What is the multiplier?
How many 0’s?

14. Recurring Decimal  Fraction 13 4 5 2 6 … ˙
… = x
… = x
… = x
1000 ˙
10000 ˙
100000
Now the engine as well as one compartment
is before the decimal point.
What is the multiplier?
How many more 0’s were needed to move
one compartment?

15. Recurring Decimal  Fraction 13 4 5 2 6 … 3 4 5 2 6 … ˙
… = x
26.345… = x
= x =
100000 ˙ – (–
100 ) ˙
99900
26319 ˙
99900

16. Recurring Decimal  Fraction 13 4 5 2 6 … =
99900
26139 ˙
Number on top?
How many 0’s?
How many 9’s?
engine and one compartment
– only engine 3 4 5 2 6 …
26345
– 26
No. of engine-windows
No. of compartment-windows

17. Recurring Decimal  Fraction 27 3 … =
What number is before the decimal point?
Now what number is before the decimal point?
Is the engine before the decimal point?
Now?
703 – 7
696 ˙ =
10000 –
100
9900
What is the multiplier?
What is the multiplier now?

18. Recurring Decimal  Fraction 32 3 9 …
0.923 =
What number is before the decimal point?
Now what number is before the decimal point?
Is the engine before the decimal point?
Nothing means which number?
923 –
923 ˙ =
1000 – 1
999
What is the multiplier?
What is the multiplier now?

19. Recurring Decimal  Fraction 48 1 5 …
0.815 =
What number is before the decimal point?
Now what number is before the decimal point?
Is the engine before the decimal point?
Now?
815 – 8
807
269 ˙ = =
1000 – 10
990
330
What is the multiplier?
What is the multiplier now?
330
269 +
330
269
= 2 ˙ ˙
2.815 = = 2