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## Lesson 13 & 14: Converting Between Fractions and Decimals

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**Lesson 13 & 14: Converting Between Fractions and Decimals**• Students convert decimals to fractions and fractions to decimal. • Students understand that every rational number can be converted to a decimal. • Students represent decimals as either terminating or repeating.**Numbers in the Real World**Places where decimals are used? Places were fractions are used?**Example 1: Decimals to Fractions**• What is the value of the number 2.25? How can this number be written as a fraction or mixed number? • Rewrite the fraction in simplest form (show your steps). • What is the value of the number 2.025? How can this number be written as a mixed number? • Rewrite the fraction in simplest form (show your steps).**Your Turn**• Use place value to convert each terminating decimal to a fraction, then rewrite the fraction in its simplest form. • 0.218 c) 2.72 • 0.16 d) 0.0005**Example 2: Fractions to Decimals**• Write the number as a decimal. Describe your process. Question: How is our denominator related to place value? Goal: Try to obtain a denominator that is on the place value chart! Tenths, hundredths, thousandths, ten thousandths, etc. Write the following numbers as decimals.**Your Turn**• Convert each fraction to a decimal.**But…..**• What about… • ‒ We need a plan in case the denominator does not go in to 10, 100 or 1,000…..**Vocabulary:Terminating Decimal and Non-Terminating Decimal**• Terminating Decimal - A terminating decimal will have a finite number of digits after the decimal point. In other words, it will end. • Non-Terminating Decimal – A non-terminating decimal will not have a finite number of digits after the decimal point. In other words, it will go on forever (it may repeat numbers or it may not repeat numbers).**Explore**Why does the division bar help us? So if we ever need to find a decimal from a given fraction, we can simply divide! • Using the division button on your calculator, find the decimal equivalents for the following fractions. • Now sort them in to the correct column. Terminating Non-Terminating**Fractions to Decimals….By dividing**• Use long division to convert the following fractions to decimals. ‒ -