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1. Place Value Powers of 10. Can help us represent decimals as fractions: 0.2, 0.45, 0.20, 4.6, etc.

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**Decimals Most decimal numbers are rational numbers: but some are not.**

A decimal is a rational number if it can be written as a fraction. So, those are decimals that either terminate (end) or repeat. Repeating decimals: …; … Terminating decimals: 4.8; ; 0.75

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A decimal like … is not rational because although there is a pattern, it does not repeat. It is irrational Compare this to … It is rational because 556 repeats. It is rational.

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**When decimals are equal**

3.56 = But, ≠ To see why, examine the place values. 3.056 = • • • .001 3.560 = • • • .001 Think of units, rods, flats, and cubes.

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**Ways to compare decimals**

Write them as fractions and compare the fractions as we did in the last section. Use base-10 blocks. Write them on a number line. Line up the place values.

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**Rounding 3.784: round this to the nearest hundredth.**

Well, is between 3.78 and On the number line, which one is closer to? 3.785 is half way in between.

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**Adding and Subtracting Decimals**

Same idea as with fractions: the denominator (place values) must be common. So, is really like ones tenths hundredths = 5.55

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**Multiplying Decimals Easiest to see with the area model. 2.1 • 1.3**

1 + .3

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**3. When decimals are equal**

3.56 = But, ≠ To see why, examine the place values. 3.056 = • • • .001 3.560 = • • • .001 Think of units, rods, flats, and cubes-how could we use them here?

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**4, Ways to compare decimals**

Write them as fractions and compare the fractions as we did in the last section. Use base-10 blocks. Write them on a number line. Line up the place values.

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**5. Rounding 3.784: round this to the nearest hundredth.**

Well, is between 3.78 and On the number line, which one is closer to? 3.785 is half way in between.

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**6. Adding and Subtracting Decimals**

Same idea as with fractions: the denominator (place values) must be common. So, is really like ones tenths hundredths = 5.55

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**7. Multiplying Decimals Easiest to see with the area model. 2.1 • 1.3**

1 + .3

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**4, Ways to compare decimals**

Write them as fractions and compare the fractions as we did in the last section. Use base-10 blocks. Write them on a number line. Line up the place values.

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**5. Rounding 3.784: round this to the nearest hundredth.**

Well, is between 3.78 and On the number line, which one is closer to? 3.785 is half way in between.

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**6. Adding and Subtracting Decimals**

Same idea as with fractions: the denominator (place values) must be common. So, is really like ones tenths hundredths = 5.55

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**7. Multiplying Decimals Easiest to see with the area model. 2.1 • 1.3**

1 + .3

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