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Chapter 3 - Decimals Math Skills – Week 4

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**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

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**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???)…

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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 .

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**Multiplication of Decimals**

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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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