Recurring Decimals – Converting – Demonstration This resource provides animated demonstrations of the mathematical method. Check animations and delete slides not needed for your class.

0. 4 1𝑥= 0.44… 10𝑥= 4.44… 9𝑥= 4 4 9 𝑥= × 10 Subtract 1𝑥 ÷ 9 DEMO Converting Recurring Decimals to Fractions Convert this decimal to a fraction. 0. 4 1𝑥= 0.44… × 10 10𝑥= 4.44… Subtract 1𝑥 9𝑥= 4 ÷ 9 4 9 𝑥= Simplify if possible.

0. 7 1𝑥= 0.77… 10𝑥= 7.77… 9𝑥= 7 7 9 𝑥= × 10 Subtract 1𝑥 ÷ 9 DEMO Converting Recurring Decimals to Fractions Convert this decimal to a fraction. 0. 7 1𝑥= 0.77… × 10 10𝑥= 7.77… Subtract 1𝑥 9𝑥= 7 ÷ 9 7 9 𝑥= Simplify if possible.

DEMO Converting Recurring Decimals to Fractions YOUR TURN Convert this decimal to a fraction. Convert this decimal to a fraction. 0. 7 0. 2 1𝑥= 0.77… 1𝑥= 0.22… × 10 × 10 10𝑥= 7.77… 10𝑥= 2.22… Subtract 1𝑥 Subtract 1𝑥 9𝑥= 7 9𝑥= 2 ÷ 9 ÷ 9 7 9 2 9 𝑥= 𝑥= Simplify if possible. Simplify if possible.

DEMO Converting Recurring Decimals to Fractions YOUR TURN Convert this decimal to a fraction. Convert this decimal to a fraction. 0. 7 0. 8 1𝑥= 0.77… 1𝑥= 0.88… × 10 × 10 10𝑥= 7.77… 10𝑥= 8.88… Subtract 1𝑥 Subtract 1𝑥 9𝑥= 7 9𝑥= 8 ÷ 9 ÷ 9 7 9 8 9 𝑥= 𝑥= Simplify if possible. Simplify if possible.

0. 2 3 1𝑥= 0.2323… 100𝑥= 23.23… 99𝑥= 23 23 99 𝑥= × 100 Subtract 1𝑥 DEMO Converting Recurring Decimals to Fractions Convert this decimal to a fraction. 0. 2 3 1𝑥= 0.2323… × 100 100𝑥= 23.23… Subtract 1𝑥 99𝑥= 23 ÷ 99 23 99 𝑥= Simplify if possible.

DEMO Converting Recurring Decimals to Fractions Convert this decimal to a fraction. 0. 4 5 1𝑥= 0.4545… × 100 100𝑥= 45.45… Subtract 1𝑥 99𝑥= 45 ÷ 99 45 99 𝑥= Simplify if possible. = 5 11

DEMO Converting Recurring Decimals to Fractions YOUR TURN Convert this decimal to a fraction. Convert this decimal to a fraction. 0. 4 5 0. 5 1 1𝑥= 0.4545… 1𝑥= 0.5151… × 100 × 100 100𝑥= 45.45… 100𝑥= 51.51… Subtract 1𝑥 Subtract 1𝑥 99𝑥= 45 99𝑥= 51 ÷ 99 ÷ 99 45 99 51 99 𝑥= 𝑥= Simplify if possible. Simplify if possible. = 5 11

DEMO Converting Recurring Decimals to Fractions YOUR TURN Convert this decimal to a fraction. Convert this decimal to a fraction. 0. 4 5 0. 3 9 1𝑥= 0.4545… 1𝑥= 0.3939… × 100 × 100 100𝑥= 45.45… 100𝑥= 39.39… Subtract 1𝑥 Subtract 1𝑥 99𝑥= 45 99𝑥= 39 ÷ 99 ÷ 99 45 99 39 99 𝑥= 𝑥= Simplify if possible. Simplify if possible. = 5 11 = 13 33

DEMO Converting Recurring Decimals to Fractions Convert this decimal to a fraction. 0. 3 2 7 1𝑥= 0.327… × 1000 1000𝑥= 327.327… Subtract 1𝑥 999𝑥= 327 ÷ 999 327 999 𝑥= Simplify if possible.

DEMO Converting Recurring Decimals to Fractions Convert this decimal to a fraction. 0. 6 3 3 1𝑥= 0.633… × 1000 1000𝑥= 633.633… Subtract 1𝑥 999𝑥= 633 ÷ 999 633 999 𝑥= Simplify if possible. = 211 333

DEMO Converting Recurring Decimals to Fractions YOUR TURN Convert this decimal to a fraction. Convert this decimal to a fraction. 0. 6 3 3 0. 2 9 8 1𝑥= 0.633… 1𝑥= 0.298… × 1000 × 1000 1000𝑥= 633.633… 1000𝑥= 298.298… Subtract 1𝑥 Subtract 1𝑥 999𝑥= 633 999𝑥= 298 ÷ 999 ÷ 999 633 999 298 999 𝑥= 𝑥= Simplify if possible. Simplify if possible. = 211 333

DEMO Converting Recurring Decimals to Fractions YOUR TURN Convert this decimal to a fraction. Convert this decimal to a fraction. 0. 6 3 3 0. 1 8 9 1𝑥= 0.633… 1𝑥= 0.189… × 1000 × 1000 1000𝑥= 633.633… 1000𝑥= 189.189… Subtract 1𝑥 Subtract 1𝑥 999𝑥= 633 999𝑥= 189 ÷ 999 ÷ 999 633 999 189 999 𝑥= 𝑥= Simplify if possible. Simplify if possible. = 211 333 = 63 333 = 21 111

Converting Recurring Decimals to Fractions Convert this decimal to a fraction. 0.1 6 1𝑥= 0.1666… × 10 10𝑥= 1.666… Subtract 1𝑥 9𝑥= 1.5 ÷ 9 1.5 9 = 15 90 𝑥= Simplify if possible. = 1 6

Converting Recurring Decimals to Fractions Convert this decimal to a fraction. 0.0 3 6 1𝑥= 0.03636… × 100 100𝑥= 3.636… Subtract 1𝑥 99𝑥= 3.6 ÷ 99 3.6 99 = 36 990 𝑥= Simplify if possible. = 4 110 = 2 55

Converting Recurring Decimals to Fractions Convert this decimal to a fraction. 0.20 8 1𝑥= 0.20888… × 10 10𝑥= 2.08888… Subtract 1𝑥 9𝑥= 1.88 ÷ 9 1.88 9 = 188 900 𝑥= Simplify if possible. = 94 450 = 47 225

DEMO Converting Recurring Decimals to Fractions YOUR TURN Convert this decimal to a fraction. 0. 5 = 0. 2 3 = 0. 4 5 1𝑥= 0.4545… × 100 100𝑥= 45.45… 0. 2 1 5 = 0.4 6 = Subtract 1𝑥 99𝑥= 45 ÷ 99 45 99 𝑥= 0.0 4 5 = 2. 7 8 = Simplify if possible. = 5 11

DEMO Converting Recurring Decimals to Fractions YOUR TURN Convert this decimal to a fraction. 0. 5 = 5 9 0. 2 3 = 23 99 0. 4 5 1𝑥= 0.4545… × 100 100𝑥= 45.45… 0. 2 1 5 = 215 999 0.4 6 = 7 15 Subtract 1𝑥 99𝑥= 45 ÷ 99 45 99 𝑥= 0.0 4 5 = 1 22 2. 7 8 = 92 33 Simplify if possible. = 5 11

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