Decimals%20and%20place%20value

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 7.6666 0.727272
• Terminating decimals 4.8 9.00001 0.75

3
Irrational numbers

• A number that is not rational is called
  irrational.
• A decimal like 3.5655655565555655556 is not
  rational because although there is a pattern, it
  does not repeat. It is an irrational number.
• Compare this to 3.556556556556556556It is
  rational because 556 repeats. It is a rational
  number.

4
Comparing Decimals

• When are decimals equal?
• 3.56 3.56000000
• But, 3.056 ? 3.560.
• To see why, examine the place values.
• 3.056 3 0 .1 5 .01 6 .001
• 3.560 3 5 .1 6 .01 0 .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. 308-323 in the textbook
• Exploration 5.16

8
Rounding

• 3.784 round this to the nearest hundredth.
• 3.784 is between 3.78 and 3.79. On the number
  line, which one is 3.784 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, 3.46 2.09 is really like3 2 ones 4
  0 tenths 6 9 hundredths 5.55

10
Multiplying Decimals

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

11
Dividing decimals

• Standard algorithmwhy 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