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**Decimals and place value**

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**Decimals as rational numbers**

Some decimal numbers are rational numbers: but some are not. A decimal is a rational number if it can be written as a fraction with integer numerator and denominator. Those are decimals that either terminate (end) or have a repeating block of digits. Repeating decimals: …; … Terminating decimals: 4.8; ; 0.75

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**Irrational numbers A number that is not rational is called irrational.**

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

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**Comparing Decimals When are decimals equal? 3.56 = 3.56000000**

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. Use a number line. Line up the place values.

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Exploration 5.16 Use the base 10 blocks to represent decimal numbers and justify your answers. Work on this together and turn in on Wednesday.

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**Homework for Wednesday**

Read pp in the textbook Exploration 5.16

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

3.784 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 2.1 • 1.3**

As with whole numbers and fractions, multiplication of decimals is best illustrated with the area model. 2.1 • 1.3 1 + .3

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Dividing decimals Standard algorithm—why do we do what we do?

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Exploration 5.18 Work on this exploration in class and finish for homework. Part 1: 1-4 Part 2: 1, 2

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