Algebra – Writing recurring decimals as fractions

©"Maths"Excel"Class"2016" 1" 4th"Yr"Mary"

Example 1 Write 0. 2 as a fraction. 0. 2 = 0.222222… Let: & = 0.222222222… (1) 10& = 2.222222222… (2) 2 − 1 The recurring numbers beyond the decimal point cancel.

9& = 2.0 & = 2

9 ∴ 0. 2 = 29

Example 2 Write 0. 15 as a fraction. 0. 15 = 0.1515151515… Let: & = 0.1515151515… (1) 100& = 15.1515151515… (2) 2 − 1

99& = 15 & = 15

99 =533 ∴ 0. 15 = 5

33 Example 3 Write 0.25 as a fraction. 0.25 = 0.25555555… Let: & = 0.25555555555… 10& = 2.55555555555… (1) 100& = 25.5555555555… (2) 2 − 1

90& = 23 & = 23

90 ∴ 0.25 = 2390

Algebra – Writing recurring decimals as fractions

©"Maths"Excel"Class"2016" 2" 4th"Yr"Mary"

Write the following as fractions: a.! 0. 1 b.! 0. 7 c.! 0. 21 d.! 0.48

e.! 0.23

f.! 0.123 g.! 0.116 h.! 0.03