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Warm-Up 29 1/ /5 29 1/7 = / /7 = / /7 = 13.

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**Decimals Many decimal numbers are rational numbers: but most 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. All fractions can be represented by terminating or repeating decimals!

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**When decimals are equal**

3.56 = But, ≠ To see why, examine the place values. 3.056 = • • • .001 whole tenths hundredths thousandths 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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Language Write down (in words) how you would say 0.5 Does 1/3 = 0.33?

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Connections

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Exploration 5.16 Do #2, 4, 7, and 8.

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

Look at the hundredths. 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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**Practice Rounding Round to the nearest tenth: 5.249**

Closer to 5.2 or 5.3? Round to the nearest hundredth: Closer to 5.24 or 5.25? Round to the nearest whole: Closer to 357 or 358? Round to the nearest hundred: Closer to 300 or 400?

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**Practice Rounding Round to the nearest thousandth: 5.0099**

Must have the last 0 for the thousandths place! Round to the nearest hundredth: 64.28 Round to the nearest tenth: 11.0 Must have the last 0 for the tenths place!

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