Recurring Decimal Fraction Recurring Decimal Representing Recurring Decimal
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Recurring Decimal Fraction Recurring Decimal Representing Recurring Decimal Fraction
Fraction Recurring Decimal 43/10 = 4. 3 10 = 2 x 5 5/8 = 0. 625 8=2 x 2 x 2 31/25 = 1. 24 25 = 5 x 5 7/3 = ?
Fraction Recurring Decimal 1 7/3 = 2. 33 …
Fraction Recurring Decimal 2 4/11 = 0. 363 …
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)
Representing Recurring Decimal 1 0. 26345345345345345. . . 2 6 3 4 5 How many windows in the engine? 2 No. of engine-windows =2 No. inofthe compartment-windows =3 3 How many windows compartment? . . = 0. 26345. . 0. 26345345… = 0. 26345
Representing Recurring Decimal 2 No. of engine-windows = 1 No. of compartment-windows = 1 0. 9444444… = 0. 94444… 9 4 4 … = 0. 94˙ 0. 94444… = 0. 94˙
Representing Recurring Decimal 3 No. of engine-windows = 1 0. 81515… No. of compartment-windows = 2 = 0. 81515… 8 1 5 1 5 … ˙˙ = 0. 815 ˙˙ 0. 8151515… = 0. 815 ˙˙ 2. 8151515… = 2. 815
Representing Recurring Decimal 4 0. 26373737… No. of engine-windows = 2 No. of compartment-windows = 2 = 0. 263737… 2 6 3 7 3 7 … ˙˙ = 0. 2637 ˙˙ 0. 263737… = 0. 2637
Representing Recurring Decimal 5 No. of engine-windows = 0 0. 923923923… No. of compartment-windows = 3 = 0. 923923… 9 2 3 … ˙ ˙ = 0. 923 There is no engine like previous examples, imagine a small one as in local trains ˙ ˙ 0. 923923923… = 0. 923
Representing Recurring Decimal 6 No. of engine-windows = 2 No. of compartment-windows = 2 0. 0703030… = 0. 070303… 0 7 0 3 0 3 … ˙˙ = 0. 0703 ˙˙ 0. 070303… = 0. 0703
Representing Recurring Decimal 4 45 41 45 … 9 8 1 29 62 33 79 32 173 5 3 … 7 … 02 76 03 34 05 33 … 04 35 … … ˙ 0. 94444… = 0. 94 ˙˙ 0. 81515… = 0. 815 ˙˙ 0. 26373737… = 0. 2637 ˙ ˙ 0. 923923923… = 0. 923 ˙˙ 0. 07030303… = 0. 0703 ˙ ˙ 0. 26345345. . . = 0. 26345
Recurring Decimal Fraction 1 2 6 3 4 5 … ˙ ˙x 1 0. 261345345… = 0. 26345 ˙ ˙ x 10 2. 63453453… = 0. 26345 ˙ ˙ x 100 26. 34534534… = 0. 26345 Now the engine is before the decimal point. What is the multiplier? How many 0’s?
Recurring Decimal Fraction 1 2 6 3 4 5 … ˙ ˙ x 1000 263. 45345345… = 0. 26345 ˙ ˙ x 10000 2634. 53453453… = 0. 26345 ˙ ˙ x 100000 26345. 34534534… = 0. 26345 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?
Recurring Decimal Fraction 1 2 6 3 4 5 … 2 6 3 4 5 3 4 ˙ ˙ x 100000 26345. 345… = 0. 26345 ˙ ˙ x (– 100) – 26. 345… = 0. 26345 ˙ ˙ x 99900 26319 = 0. 26345 26319 ˙ ˙ = 0. 26345 99900 5 …
Recurring Decimal Fraction 1 2 ˙ ˙= 0. 26345 6 3 26139 99900 4 5 3 4 5 … Number on top? How many 0’s? How many 9’s? engine and one compartment 2 6 3– only 4 engine 5 3 4 26345 5 … – 26 No. of engine-windows No. of compartment-windows
Recurring Decimal Fraction 2 0 7 0 3 0 3 … What. Now number isnumber before is the decimal point? what before the decimal point? Is the engine before the decimal point? Now? – 7 703 696 ˙˙ 0. 0703 = = 10000 – 100 9900 What is the multiplier? What is the multiplier now?
Recurring Decimal Fraction 3 9 2 3 … What number is beforeisthe decimal point? Now what number before the decimal Is the engine before the decimal point? Nothing means which number? – 0 923 ˙ ˙ 0. 923 = = 1000 – 1 999 What is the multiplier? What is the multiplier now?
Recurring Decimal Fraction 4 8 1 5 1 5 … What number is before the decimalthe point? Now what number is before decimal point? Is the engine before Now? the decimal point? – 8 815 807 269 ˙˙ 0. 815 = = = 1000 – 10 990 330 What is the multiplier? What is the multiplier now? 269 ˙˙ = 2 + 0. 815 ˙˙ = 2 + =2 2. 815 330
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