Recurring decimals.pptx
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Recurring decimals can be converted to fractions by representing the repeating decimal as an equation and multiplying both sides by a power of 10 to eliminate the decimal point, then solving for the variable. For example, to convert 0.1, we write 0.1 = x, multiply both sides by 10 to get 1.1 = 10x, then solve to find x = 1/9, representing 0.1 as the fraction 1/9.
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- 1. Recurring decimals Grade 9 By Mr Tono
- 2. Converting recurring decimals to fractions Converting recurring decimals to fractions is representing a recurring decimal as a fraction without changing its value. A recurring decimal is a decimal number that has a digit (or group of digits) that repeats forever. The part that repeats can also be shown by placing dots over the first and last digits of the repeating pattern.
- 3. E.g. are all recurring decimals
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- 5. Example 1 Convert 0. 1 to a fraction
- 6. 0. 1 = 𝑥 Equation 1 Because 0. 1 = 𝑥 has one repeating digit, we will multiply by 10 0. 1 × 10 = 1. 1 Remember because you are multiplying the whole of Equation 1 you also need to multiply the variable 𝑥 by 10 (see below) 0. 1 = 𝑥 Equation 1 0. 1 × 10 = 𝑥 × 10 1. 1 = 10𝑥 Equation 2
- 7. 1. 1 = 10𝑥 Equation 2 0. 1 = 𝑥 Equation 1 1 = 9𝑥 1 = 9𝑥 1 9 = 𝑥