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DECIMALS

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WHAT ARE DECIMALS? We’ve done lots of work with fractions. Now we are going to talk about decimals. Decimals give us a way to write special fractions that have denominators of 10, 100, 1,000, 10,000, or even 100,000,000,000! The special denominators are all powers of 10.

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DECIMALS ON GRIDS Below is a hundredths grid. How many squares are shaded? How do we write this as a fraction? How do we write this as a decimal?

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Let’s look at another shaded grid. Write this amount as a fraction and a decimal.

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Can the shaded amount on this grid be written more than one way?

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PLACE VALUE CHART—LET’S PRACTICE READING SOME NUMBERS!

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NOW LET’S READ SOME NUMBERS (ONLY USE YOUR CHART IF YOU NEED TO)

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WRITING DECIMALS Now that we’ve practiced reading decimals, let’s write some decimals in words. Watch your spelling!

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HOW DO YOU WRITE FRACTIONS AS DECIMALS? As we discussed earlier, decimals are fractions written with denominators that are powers of 10. Some fractions are easy to change to decimals because their denominators are factors of a power of 10. Let’s try. 1/4 = 2/5= 5/8= 7/20= 31/10 =

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DENOMINATORS THAT AREN’T FACTORS OF A POWER OF 10 What happens if you have to change a fraction to a decimal, but its denominator isn’t a number that is easily changed to a power of 10? You can change these fractions to decimals by dividing the numerator by the denominator. (Remember: A fraction is a way to write a division problem.) Let’s try with 2/3. What do you notice about the decimal equivalent for this fraction? This type of decimal is called a repeating decimal. A decimal that has digits that do not go on forever is called a terminating decimal.

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WRITING DECIMALS AS FRACTIONS We’ve changed fractions to decimals, now let’s write decimals as fractions. Start by reading the decimal either in your head or out loud. Let’s try. Read the following number Write what you read as a fraction. Finally, simplify.

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FINDING NUMBERS BETWEEN DECIMALS Finding decimals between decimals isn’t as hard as you might think. Just remember this: YOU CAN ADD AS MANY ZEROS AS YOU WANT TO THE END OF A DECIMAL NUMBER, AND ITS VALUE WILL NOT CHANGE. Find a decimal between 0. 8 and Find a decimal between 0.6 and 0.7 Find a decimal between 1.1 and 1.25

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DECIMAL BENCHMARKS What are some fractions that you already know the decimal equivalents of? Let’s turn to page 42 in our books to look at some decimal benchmarks.

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ORDERING DECIMALS If you remember that you can add as many zeros as you want to the end of a decimal number, you shouldn’t have a problem putting decimals in order. Just add zeros until your list of numbers is easier to compare. Let’s try. Put the following numbers in order from least to greatest

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