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 = • • • .0013.560 = • • • .001Think 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 5.16Use 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 textbookExploration 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 • 1.31+.3
11 Dividing decimalsStandard algorithm—why do we do what we do?
12 Exploration 5.18Work on this exploration in class and finish for homework.Part 1: 1-4Part 2: 1, 2