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Converting a repeating decimal to a fraction

Converting a repeating decimal to a fraction. ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction?. Vocabulary – Shoot For The Stars 30 seconds.

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Converting a repeating decimal to a fraction

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  1. Converting a repeating decimal to a fraction

  2. ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction? Vocabulary –Shoot For The Stars 30 seconds • I got this! I know this word AND I could even teach it to somebody else. • I think I know this word, but I need more practice. • I am clueless! I have no idea what this word means.

  3. ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction? Vocabulary • Repeating Decimal - a decimal in which a figure or group of digits is repeated in a pattern forever, as in 0.333… • Variable - A symbol for a number we don't know yet. It is usually a letter like x or y. • Equation – A statement indicating the equality of two expressions. It is split into left and right sides joined by an equal sign.

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  6. ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction? Recurring Decimals All recurring decimals can be written as fractions. In other words, you can write it on a piece of paper using a bar. They are ‘rational numbers’

  7. ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction? Recurring Decimals Since you can write A recurring decimal As a fraction on a piece of paper, it is Rational.

  8. ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction? Recurring Decimals To write recurring decimals as fractions, we use a simple multiplying method called… Ten Again Ten

  9. ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction? Recurring Decimals To do so, you keep multiplying by 10 until the ending part of the decimals are the same …

  10. ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction? Recurring Decimals e.g. 0.333333333… Let x = 0.333333333… Keep multiplying by 10 until the ending part of the decimals are the same … Sooooo 10x = 3.333333…

  11. ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction? Recurring Decimals Then… Subtract the two variable expressions that contain similar decimal endings.

  12. ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction? Recurring Decimals 10x = 3.33333333… - x = 0.33333333… 9x = 3 X = 3 = 1 9 3

  13. ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction? Recurring Decimals e.g. 0.565656… Let x = 0.5656565… 10x = 5.65656565… 100x = 56.56565656… Which two have similar endings?…

  14. ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction? Recurring Decimals Now Subtract 100x = 56.56565656… - x = 0.565656565 99x = 56 X = 56 99

  15. ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction? Recurring Decimals Reminder: Recurring decimals are written by using a bar: e.g. 0.3333333…. = 0.3 e.g. 0.8474747…= 0.847

  16. ESSENTIAL QUESTION: Why is a repeating decimal a rational number? What is the process of converting a repeating decimal to a fraction? Now you try • Convert the decimals to fractions • 0.545454….. • 0.599999…. • 0.345555…. • 0.222…

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