6 days of class left Final Exam Tuesday December 14 th 24 Decimals Ratio and Proportion Percents Problem Solving Decimals and place value Expanded form 324 0183 24750 Exploration 516 ID: 257284
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Slide1
The end is near
6 days of class left
Final Exam Tuesday, December 14
th
, 2-4
Decimals
Ratio and Proportion
Percents
Problem SolvingSlide2
Decimals and place valueSlide3
Expanded form
3.24
0.183
24.750Slide4
Exploration 5.16
Use base 10 blocks to do #1-3Slide5
Rational Numbers
As fractions:
As decimals:Slide6
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 7/8Slide7
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 Slide8
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
.Slide9
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.Slide10
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.Slide11
Exploration 5.16
#8 Comparing decimalsSlide12
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.
3.78 3.785 3.79Slide13
Adding and Subtracting
Decimal Numbers
Exploration 5.16
Use the base 10 blocks to do #4 and #5Slide14
Adding and Subtracting
Decimal Numbers
3.46 + 2.09
25.4 − 13.67Slide15
Multiplying Decimals
Exploration 5.16
#6 and #7Slide16
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.Slide17
Standard Algorithm for
Multiplying Decimals
Why do we do what we do?
Multiply 2.1
× 1.3
Explain the algorithm.Slide18
Dividing Decimal Numbers
What model should we use?Slide19
Dividing decimals
Standard algorithm—why do we do what we do?
Divide: 25.92
÷ 1.2Slide20
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