1. Chapter 3 - Decimals
Math Skills – Week 4

2. Outline Introduction to Decimals – Section 3.1
Addition of Decimals – Section 3.2
Subtraction of Decimals – Section 3.3
Multiplication of Decimals – Section 3.4
Division of Decimals – Section 3.5
Comparing and Converting Fractions and Decimals – Section 3.6
Outline

3. Stuff to Remember (forget???)…
Reduce all fractional answers to simplest form, and convert improper fractions to mixed numbers
MIDTERM Next Class
Chapters 1, 2, and 3
Study tips
review slides
your notes
read sections in the book
look at example problems in book
Pay attention to what question is asking
Prime factorization vs. Finding all factors
On homework/quizzes, clearly circle your answer
Class Project Handout
Stuff to Remember (forget???)…

4. Introduction to Decimals
This is a number in decimal notation
The decimal part represents a number less than one
Just like… $61.88, 88 represents 88 cents, which is less than $1.
61.88
Decimal
part
Whole Number part
Decimal Point
Introduction to Decimals

5. Introduction to Decimals
Just as with whole numbers, decimal numbers have place values:
The position of a digit in a decimal determines the digits place value
0 is in the hundredths, 3 is in the tenths
9 is in the _______ place
4 is in the _______ place
hundreds
tens
ones
tenths
hundredths
Ten-thousandths
hundred-thousandths
thousandths
millionths . 4 5 8 3 2 7 1 9
millionths
hundredths
Introduction to Decimals

6. Introduction to Decimals
Rounding decimals is similar to rounding whole numbers.
Approximate the decimal to any place value
Steps
Write out the number to be rounded in a place value chart
Look at the number to the right of the place value you are rounding to.
If the number is > or = 5, increase the digit in the place value by 1, and remove all digits to the right of it
If the number is < 5, remove it and all of the digits to the right of it.
Examples
Round to the nearest thousandth
0.470
Round to nearest hundred thousandths
Introduction to Decimals

7. Introduction to Decimals
Class Examples
Round to the nearest tenth
48.9
Round to the nearest whole number 32
Round to the nearest ten- thousandth
3.6758
Introduction to Decimals

8. Addition/Subtraction of Decimals
Adding and subtracting decimal numbers is the similar as adding and subtracting whole numbers
Catch: first align the decimal points of each number on a vertical line.
Assures us that we are adding/subtracting digits that are in the same place value
4290.3
000
Addition/Subtraction of Decimals

9. Addition/Subtraction of Decimals
Examples (Addition)
Add: =
Add: =
Class Examples (Addition)
Find the sum of 4.62, 27.9, and =
Add: =
Addition/Subtraction of Decimals

10. Addition/Subtraction of Decimals
Examples (Subtraction)
Subtract: – 7.96 =
Find 9.23 less than 29
= 19.77
Class Examples (Subtraction)
Subtract – 8.47 =
Subtract 35 – 9.67
= 25.33
Addition/Subtraction of Decimals

11. Multiplication of Decimals
Multiplication of decimals is similar to multiplication of whole numbers.
Question: Where does decimal go?
Check this…
0.3 x 5 = 1.5
Start with 1 decimal place, answer has 1 decimal place
0.3 x 0.5 = 0.15
Start with a total of 2 decimal places, answer has 2 decimal places
0.3 x 0.05 = 0.015
Start with a total of 3 decimal places, answer has 3 decimal places
Multiplication of Decimals

12. Multiplication of Decimals
Multiplication Steps
Do the multiplication as if it were whole numbers
To place the decimal in the right location
Count the total number of decimal places in all of the factors
Starting from the right of the product, count the total number of decimal places towards the left, and place the decimal point there.
21.4
x 0.36
3 total decimal places
Multiplication of Decimals
7 704 .

13. Multiplication of Decimals
Examples
920 x 3.7 =
x 0.025 =
Class Examples
870 x 4.6 =
x 0.057 =
Multiplication of Decimals

14. Multiplication of Decimals
To multiply a decimal by a power of 10 (for example 10, 100, 1,000 etc.) move the decimal to the right the same number of times as there are zeros.
x 10 =
x 100 =
x 1000 =
x 10000 = x
= (Note: we added a zero before the decimal)
Multiplication of Decimals

15. Dividing decimals is similar to dividing whole numbers.
Same question…what about the decimal place? Where does that go?
Steps
Make the divisor a whole number by shifting the decimal to the right as many times as necessary.
Move the decimal in the dividend the same number of times that we moved it in the divisor
7 0 6 . .
??????
Division of Decimals

16. Division of Decimals Dividing decimals…contd 706 42090.00 706
Steps
Add zeros to the end of the dividend so that we can round to the desired place value
Example: Round quotient to nearest tenth  write 2 zeros after the decimal
Round quotient to nearest thousandth  need 4 zeros after the decimal
706
706
Division of Decimals

17. Division of Decimals Dividing decimals…contd 00059.61 ≈ 59.6 706
Steps
Do the division as if it were whole numbers
Put the decimal place in the quotient directly over the decimal point in the dividend
≈ 59.6
706
Division of Decimals

18. Division of Decimals Examples
Divide ÷ 82 round to the nearest thousandth
= ≈ 0.708
Divide: ÷ 7.06, round to the nearest tenth
= ≈ 59.6
Divide: ÷ 0.039, round to the nearest hundredth
≈ 55.85
Division of Decimals

19. Division of Decimals Class Examples
Divide ÷ 76 round to the nearest thousandth
= ≈ 0.487
Divide: ÷ 5.09, round to the nearest tenth
= ≈ 72.7
Division of Decimals

20. To divide a decimal by a power of 10 (for example 10, 100, 1,000 etc
To divide a decimal by a power of 10 (for example 10, 100, 1,000 etc.) move the decimal to the left the same number of times as there are zeros. Fill in the blank spaces with zeros.
34.65 ÷ 10 or 101
= 3.465
34.65 ÷ 100 or 102 =
34.65 ÷ 1000 or 103 =
34.65 ÷ or 104 =
Division of Decimals

21. Comparing & Converting Fractions & Decimals
Fractions and decimals are two ways of representing parts of a whole number.
¼ is a portion of 1 whole
0.345 is a portion of 1 whole
Every fraction can be written as a decimal
Every decimal can be written as a fraction
Comparing & Converting Fractions & Decimals

22. Comparing & Converting Fractions & Decimals
To convert a fraction  decimal
Steps
Divide the numerator of the fraction by the denominator
Round the quotient to a desired place value
Example
Convert 3/7 to a decimal and round to nearest Hundredth and Thousandth =
Nearest Hundredth: 0.43
Nearest Thousandth: 0.429
Comparing & Converting Fractions & Decimals

23. Comparing & Converting Fractions & Decimals
Examples
Convert 3/8 to a decimal; round to nearest hundredth
= ≈ 0.38
Convert 2 ¾ to a decimal; round to nearest tenth
= 2.75 ≈ 2.8
Class Examples
Convert 9/16 to a decimal; round to nearest tenth
= 0.6
Convert 4 1/6 to a decimal; round to nearest hundredth
= 4.17
Comparing & Converting Fractions & Decimals

24. Comparing & Converting Fractions & Decimals
To convert a decimal  fraction
Steps
Count the number of decimal places
Remove the decimal point (and any leading zeros)
Put the decimal part over a denominator,
The denominator is a factor of 10 that has the same number of zeros as decimal places (from step 1)
Put the fraction in simplest form
Example
Convert 0.47 to a fraction
= 47/100
Convert to a fraction
275/1000 = 11/40
Comparing & Converting Fractions & Decimals

25. Comparing & Converting Fractions & Decimals
Examples:
Convert 0.82 to a fraction
= 82/100 = 2·41 / 2·50 = 41/50
Convert 4.75 to a fraction
= 4 75/100 = 4 3·25/4·25 = 4 3/4
Class Examples
Convert 0.56 to a fraction
= 56/100 = 4·14 / 4·25
Convert 5.35 to a fraction
= 5 35/100 = 5 7·5 / 5·20 = 5 7/20
Comparing & Converting Fractions & Decimals

26. Comparing & Converting Fractions & Decimals
The order relation between two decimals tells us which decimal is larger than the other
Example: Which is larger 0.88 or 0.088?
0.88
Think of this like money
0.88 is like $0.88 = 88 cents
0.088 is ≈ $0.09 = 9 cents
Comparing decimals is easy, what about comparing a decimal to a fraction?
Which is larger 5/6 or 0.625?
Question: What to do?
Convert 5/6  Decimal OR
Convert  fraction
Comparing & Converting Fractions & Decimals

27. Comparing & Converting Fractions & Decimals
Examples
Find the order relation between 3/8 and 0.38
3/8 = <  3/8 < 0.38
Class Example
Find the order relation between 5/16 and 0.32
5/16 ≈ < 0.32  5/16 < 0.32
Comparing & Converting Fractions & Decimals