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The end is near. 6 days of class left Final Exam Tuesday, December 14 th , 2-4 Decimals Ratio and Proportion Percents Problem Solving. Decimals and place value. Expanded form. 3.24 0.183 24.750. Exploration 5.16. Use base 10 blocks to do #1-3. Rational Numbers. As fractions:

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the end is near
The end is near
  • 6 days of class left
  • Final Exam Tuesday, December 14th, 2-4
  • Decimals
  • Ratio and Proportion
  • Percents
  • Problem Solving
expanded form
Expanded form

3.24

0.183

24.750

exploration 5 16
Exploration 5.16
  • Use base 10 blocks to do #1-3
rational numbers
Rational Numbers

As fractions:

As decimals:

without using a calculator
Without using a calculator:

Find the decimal representation of each of the following fractions:

1/5 ¼ 1/3

2/5 3/10 2/7

1/9 4/25 3/100

5/9 5/7 7/8

decimals as rational numbers
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
irrational numbers
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 3.556556556556556556…It is rational because 556 repeats. It is a rational number.
comparing decimals
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.
ways to compare decimals
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.
exploration 5 161
Exploration 5.16

#8 Comparing decimals

rounding

3.78 3.785 3.79

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.
adding and subtracting decimal numbers
Adding and Subtracting Decimal Numbers

Exploration 5.16

Use the base 10 blocks to do #4 and #5

multiplying decimals
Multiplying Decimals

Exploration 5.16

#6 and #7

multiplying decimals1
Multiplying Decimals

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

2.1 • 1.3

Use the grid paper to find the product.

standard algorithm for multiplying decimals
Standard Algorithm for Multiplying Decimals

Why do we do what we do?

Multiply 2.1 × 1.3

Explain the algorithm.

dividing decimal numbers
Dividing Decimal Numbers

What model should we use?

dividing decimals
Dividing decimals

Standard algorithm—why do we do what we do?

Divide: 25.92 ÷ 1.2

homework for thursday
Homework for Thursday
  • Read pp. 308-324(top) in the textbook
  • Textbook problems pp. 331-334

# 2b,d; 5b,d,f; 8, 10a,c

  • Exploration 5.16