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The end is near

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

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

  2. Decimals and place value

  3. Expanded form 3.24 0.183 24.750

  4. Exploration 5.16 • Use base 10 blocks to do #1-3

  5. Rational Numbers As fractions: As decimals:

  6. 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

  7. 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

  8. 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.

  9. 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.

  10. 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.

  11. Exploration 5.16 #8 Comparing decimals

  12. 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.

  13. Adding and Subtracting Decimal Numbers Exploration 5.16 Use the base 10 blocks to do #4 and #5

  14. Adding and Subtracting Decimal Numbers 3.46 + 2.09 25.4 − 13.67

  15. Multiplying Decimals Exploration 5.16 #6 and #7

  16. 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.

  17. Standard Algorithm for Multiplying Decimals Why do we do what we do? Multiply 2.1 × 1.3 Explain the algorithm.

  18. Dividing Decimal Numbers What model should we use?

  19. Dividing decimals Standard algorithm—why do we do what we do? Divide: 25.92 ÷ 1.2

  20. 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

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