Converting a repeating decimal to a fraction

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Presentation transcript:

Converting a repeating decimal to a fraction

Vocabulary –Shoot For The Stars 30 seconds 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.

ESSENTIAL QUESTION: Why is a repeating decimal a rational number 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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Recurring Decimals They are ‘rational numbers’ 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’

As a fraction on a piece of paper, it is 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.

ESSENTIAL QUESTION: Why is a repeating decimal a rational number 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

ESSENTIAL QUESTION: Why is a repeating decimal a rational number 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 …

Recurring Decimals e.g. 0.333333333… Let x = 0.333333333… 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…

Recurring Decimals Then… 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.

Recurring Decimals 10x = 3.33333333… - x = 0.33333333… 9x = 3 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

Recurring Decimals e.g. 0.565656… Which two have similar endings?… 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?…

Recurring Decimals Now Subtract 100x = 56.56565656… - x = 0.565656565 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

Recurring Decimals Reminder: 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

Now you try Convert the decimals to fractions 0.545454….. 0.599999…. 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…