1. Recurring Decimals – Converting – Demonstration
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2. 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.

3. 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.

4. 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.

5. 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.

6. 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.
1𝑥=
0.2323…
× 100
100𝑥=
23.23…
Subtract 1𝑥
99𝑥= 23
÷ 99
23 99 𝑥=
Simplify
if possible.

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

8. DEMO
Converting Recurring Decimals to Fractions
YOUR TURN
Convert this decimal to a fraction.
Convert this decimal to a fraction.
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

9. DEMO
Converting Recurring Decimals to Fractions
YOUR TURN
Convert this decimal to a fraction.
Convert this decimal to a fraction.
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

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

11. DEMO
Converting Recurring Decimals to Fractions
Convert this decimal to a fraction.
1𝑥=
0.633…
× 1000
1000𝑥= …
Subtract 1𝑥
999𝑥=
633
÷ 999 𝑥=
Simplify
if possible. =

12. DEMO
Converting Recurring Decimals to Fractions
YOUR TURN
Convert this decimal to a fraction.
Convert this decimal to a fraction.
1𝑥=
0.633…
1𝑥=
0.298…
× 1000
× 1000
1000𝑥= …
1000𝑥= …
Subtract 1𝑥
Subtract 1𝑥
999𝑥=
633
999𝑥=
298
÷ 999
÷ 999 𝑥= 𝑥=
Simplify
if possible.
Simplify
if possible. =

13. DEMO
Converting Recurring Decimals to Fractions
YOUR TURN
Convert this decimal to a fraction.
Convert this decimal to a fraction.
1𝑥=
0.633…
1𝑥=
0.189…
× 1000
× 1000
1000𝑥= …
1000𝑥= …
Subtract 1𝑥
Subtract 1𝑥
999𝑥=
633
999𝑥=
189
÷ 999
÷ 999 𝑥= 𝑥=
Simplify
if possible.
Simplify
if possible. = = =

14. 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

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

16. Converting Recurring Decimals to Fractions
Convert this decimal to a fraction.
0.20 8
1𝑥= …
× 10
10𝑥= …
Subtract 1𝑥
9𝑥=
1.88
÷ 9
1.88 9 = 𝑥=
Simplify
if possible. = =

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

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

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