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Decimals and place value

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Presentation on theme: "Decimals and place value"— Presentation transcript:

1 Decimals and place value

2 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

3 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.

4 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.

5 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.

6 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.

7 Homework for Wednesday
Read pp in the textbook Exploration 5.16

8 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.

9 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

10 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

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

12 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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