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Published byLesley Johnston Modified over 6 years ago
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Recurring Decimal Fraction Recurring Decimal
Representing Recurring Decimal Recurring Decimal Fraction
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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
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Fraction Recurring Decimal 1
7/3 = 2 . 3 3 …
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Fraction Recurring Decimal 2
. 3 6 3 … 4/11 =
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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)
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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 .
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Representing Recurring Decimal 2
No. of engine-windows = 1 … … = 0.94 No. of compartment-windows = 1 = … 9 4 4 … = 0.94 ˙ ˙
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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 ˙ ˙ ˙
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Representing Recurring Decimal 4
No. of engine-windows = 2 … … = No. of compartment-windows = 2 = … 6 2 3 7 3 7 … = ˙ ˙
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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 ˙
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Representing Recurring Decimal 6
No. of engine-windows = 2 … … = No. of compartment-windows = 2 = … 7 3 3 … = ˙ ˙
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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 ˙ = ˙ = ˙
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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?
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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?
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Recurring Decimal Fraction 1
3 4 5 2 6 … 3 4 5 2 6 … ˙ … = x 26.345… = x = x = 100000 ˙ – (– 100 ) ˙ 99900 26319 ˙ 99900
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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
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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?
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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?
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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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