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Recurring Decimal Fraction  Recurring Decimal

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Presentation on theme: "Recurring Decimal Fraction  Recurring Decimal"— Presentation transcript:

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 Decimal
9 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 1
3 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 1
3 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 1
3 4 5 2 6 3 4 5 2 6 ˙ … = x 26.345… = x = x = 100000 ˙ (– 100 ) ˙ 99900 26319 ˙ 99900

16 Recurring Decimal  Fraction 1
3 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 2
7 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 3
2 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 4
8 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


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