Chapter 3 - Decimals Math Skills – Week 4. Outline Introduction to Decimals – Section 3.1 Addition of Decimals – Section 3.2 Subtraction of Decimals –

Chapter 3 - DecimalsChapter 3 - DecimalsMath Skills ndash Week 4

OutlineOutline

Introduction to Decimals ndash Section 31Addition of Decimals ndash Section 32Subtraction of Decimals ndash Section 33Multiplication of Decimals ndash Section 34Division of Decimals ndash Section 35Comparing and Converting Fractions and

Decimals ndash Section 36

Stuff to Remember (forget)hellipStuff to Remember (forget)hellip

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 bookPay attention to what question is asking

Prime factorization vs Finding all factorsOn homeworkquizzes clearly circle your answerClass Project Handout

Introduction to DecimalsIntroduction to Decimals

This is a number in decimal notation

The decimal part represents a number less than one

Just likehellip $6188 88 represents 88 cents which is less than $1

6188Whole Number part

Decimal Point

Decimal part


Just as with whole numbers decimal numbers have place values

The position of a digit in a decimal determines the digits place value0 is in the hundredths 3 is in the tenths9 is in the _______ place4 is in the _______ place

4 5 8 3 0 2 7 1 9

hundre

ds

tens

ones

tenth

s

hundre

dth

s

thousa

ndth

s

Ten-

thousa

ndth

s

hundre

d-

thousa

ndth

s

mill

ionth

s

millionthshundredths


Rounding decimals is similar to rounding whole numbers

Approximate the decimal to any place value Steps

1 Write out the number to be rounded in a place value chart

2 Look at the number to the right of the place value you are rounding to

1 If the number is gt or = 5 increase the digit in the place value by 1 and remove all digits to the right of it

2 If the number is lt 5 remove it and all of the digits to the right of itExamples

Round 046972 to the nearest thousandth 0470

Round 0635457 to nearest hundred thousandths 063546


Class Examples Round 48907 to the nearest tenth

489 Round 318562 to the nearest whole number

32 Round 3675849 to the nearest ten-

thousandth 36758

AdditionSubtraction of DecimalsAdditionSubtraction 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 lineAssures us that we are addingsubtracting

digits that are in the same place value

4290316290903

+ 650729

0000

206462759


Examples (Addition)Add083 + 7942 + 15

= 23772Add 23037 + 167892

= 398262Class Examples (Addition)

Find the sum of 462 279 and 062054 = 3314054

Add 605 + 12 + 0374 = 18424


Examples (Subtraction)Subtract 39047 ndash 796

= 31087Find 923 less than 29

= 1977Class Examples (Subtraction)

Subtract 72039 ndash 847 = 63569


Multiplication of DecimalsMultiplication of Decimals

Multiplication of decimals is similar to multiplication of whole numbersQuestion Where does decimal go

Check thishellip03 x 5 = 15

Start with 1 decimal place answer has 1 decimal place

03 x 05 = 015 Start with a total of 2 decimal places answer has

2 decimal places03 x 005 = 0015

Start with a total of 3 decimal places answer has 3 decimal places


Multiplication Steps1 Do the multiplication as if it were whole

numbers2 To place the decimal in the right location

1 Count the total number of decimal places in all of the factors

2 Starting from the right of the product count the total number of decimal places towards the left and place the decimal point there

214x 036

3 total decimal places

7 704


Examples 920 x 37

= 34040000079 x 0025

= 000001975Class Examples

870 x 46 = 40020

0000086 x 0057 = 0000004902


To multiply a decimal by a power of 10 (for example 10 100 1000 etc) move the decimal to the right the same number of times as there are zeros38925 x 10

= 3892538925 x 100

= 3892538925 x 1000

= 3892538925 x 10000

= 389250 38925 x 100000

=3892500 (Note we added a zero before the decimal)

Division of DecimalsDivision of Decimals

Dividing decimals is similar to dividing whole numbers Same questionhellipwhat about the decimal place

Where does that goSteps

1Make the divisor a whole number by shifting the decimal to the right as many times as necessary

2Move the decimal in the dividend the same number of times that we moved it in the divisor

7 0 6 4 2 0 9 0


Dividing decimalshellipcontdSteps

1 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 4209000

706 420900000



1 Do the division as if it were whole numbers2 Put the decimal place in the quotient directly

over the decimal point in the dividend

706 4209000

0005961 asymp 596


ExamplesDivide 58092 divide 82 round to the nearest

thousandth = 07084 asymp 0708

Divide 4209 divide 706 round to the nearest tenth = 5961 asymp 596

Divide 2178 divide 0039 round to the nearest hundredth asymp 5585


Class ExamplesDivide 37042 divide 76 round to the nearest




To divide a decimal by a power of 10 (for example 10 100 1000 etc) move the decimal to the left the same number of times as there are zeros Fill in the blank spaces with zeros3465 divide 10 or 101

= 34653465 divide 100 or 102

= 034653465 divide 1000 or 103

= 0034653465 divide 10000 or 104

= 0003465

Comparing amp Converting Fractions Comparing amp Converting Fractions amp Decimalsamp Decimals

Fractions and decimals are two ways of representing parts of a whole number frac14 is a portion of 1 whole 0345 is a portion of 1 whole

Every fraction can be written as a decimalEvery decimal can be written as a fraction


To convert a fraction decimalSteps

1 Divide the numerator of the fraction by the denominator

2 Round the quotient to a desired place valueExample

Convert 37 to a decimal and round to nearest Hundredth and Thousandth

= 042857 Nearest Hundredth 043 Nearest Thousandth 0429


ExamplesConvert 38 to a decimal round to nearest

hundredth = 0375 asymp 038

Convert 2 frac34 to a decimal round to nearest tenth = 275 asymp 28

Class ExamplesConvert 916 to a decimal round to nearest tenth

= 06Convert 4 16 to a decimal round to nearest

hundredth = 417


To convert a decimal fractionSteps

1 Count the number of decimal places2 Remove the decimal point (and any leading zeros)3 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)

4 Put the fraction in simplest formExample

Convert 047 to a fraction = 47100

Convert 0275 to a fraction 2751000 = 1140


ExamplesConvert 082 to a fraction

= 82100 = 241 250 = 4150Convert 475 to a fraction

= 4 75100 = 4 325425 = 4 34Class Examples

Convert 056 to a fraction = 56100 = 414 425

Convert 535 to a fraction = 5 35100 = 5 75 520 = 5 720


The order relation between two decimals tells us which decimal is larger than the otherExample Which is larger 088 or 0088

088Think of this like money

088 is like $088 = 88 cents 0088 is asymp $009 = 9 cents

Comparing decimals is easy what about comparing a decimal to a fractionWhich is larger 56 or 0625

Question What to doConvert 56 Decimal OR Convert 0625 fraction


ExamplesFind the order relation between 38 and 038

38 = 0375 lt 0380 38 lt 038Class Example

Find the order relation between 516 and 032 516 asymp 0313 lt 032 516 lt 032

OutlineOutline

Introduction to Decimals ndash Section 31Addition of Decimals ndash Section 32Subtraction of Decimals ndash Section 33Multiplication of Decimals ndash Section 34Division of Decimals ndash Section 35Comparing and Converting Fractions and

Decimals ndash Section 36












Decimal Point

Decimal part




4 5 8 3 0 2 7 1 9

hundre

ds

tens

ones

tenth

s

hundre

dth

s

thousa

ndth

s

Ten-

thousa

ndth

s

hundre

d-

thousa

ndth

s

mill

ionth

s















thousandth 36758





4290316290903

+ 650729

0000

206462759



= 23772Add 23037 + 167892



Add 605 + 12 + 0374 = 18424



















214x 036


7 704


Examples 920 x 37

= 34040000079 x 0025


870 x 46 = 40020

0000086 x 0057 = 0000004902



= 3892538925 x 100

= 3892538925 x 1000

= 3892538925 x 10000

= 389250 38925 x 100000







7 0 6 4 2 0 9 0






706 4209000

706 420900000





706 4209000

0005961 asymp 596












= 34653465 divide 100 or 102

= 034653465 divide 1000 or 103

= 0034653465 divide 10000 or 104

= 0003465
















hundredth = 417











= 4 75100 = 4 325425 = 4 34Class Examples
























Decimal Point

Decimal part




4 5 8 3 0 2 7 1 9

hundre

ds

tens

ones

tenth

s

hundre

dth

s

thousa

ndth

s

Ten-

thousa

ndth

s

hundre

d-

thousa

ndth

s

mill

ionth

s















thousandth 36758





4290316290903

+ 650729

0000

206462759



= 23772Add 23037 + 167892



Add 605 + 12 + 0374 = 18424



















214x 036


7 704


Examples 920 x 37

= 34040000079 x 0025


870 x 46 = 40020

0000086 x 0057 = 0000004902



= 3892538925 x 100

= 3892538925 x 1000

= 3892538925 x 10000

= 389250 38925 x 100000







7 0 6 4 2 0 9 0






706 4209000

706 420900000





706 4209000

0005961 asymp 596












= 34653465 divide 100 or 102

= 034653465 divide 1000 or 103

= 0034653465 divide 10000 or 104

= 0003465
















hundredth = 417











= 4 75100 = 4 325425 = 4 34Class Examples


















Decimal Point

Decimal part




4 5 8 3 0 2 7 1 9

hundre

ds

tens

ones

tenth

s

hundre

dth

s

thousa

ndth

s

Ten-

thousa

ndth

s

hundre

d-

thousa

ndth

s

mill

ionth

s















thousandth 36758





4290316290903

+ 650729

0000

206462759



= 23772Add 23037 + 167892



Add 605 + 12 + 0374 = 18424



















214x 036


7 704


Examples 920 x 37

= 34040000079 x 0025


870 x 46 = 40020

0000086 x 0057 = 0000004902



= 3892538925 x 100

= 3892538925 x 1000

= 3892538925 x 10000

= 389250 38925 x 100000







7 0 6 4 2 0 9 0






706 4209000

706 420900000





706 4209000

0005961 asymp 596












= 34653465 divide 100 or 102

= 034653465 divide 1000 or 103

= 0034653465 divide 10000 or 104

= 0003465
















hundredth = 417











= 4 75100 = 4 325425 = 4 34Class Examples
















4 5 8 3 0 2 7 1 9

hundre

ds

tens

ones

tenth

s

hundre

dth

s

thousa

ndth

s

Ten-

thousa

ndth

s

hundre

d-

thousa

ndth

s

mill

ionth

s















thousandth 36758





4290316290903

+ 650729

0000

206462759



= 23772Add 23037 + 167892



Add 605 + 12 + 0374 = 18424



















214x 036


7 704


Examples 920 x 37

= 34040000079 x 0025


870 x 46 = 40020

0000086 x 0057 = 0000004902



= 3892538925 x 100

= 3892538925 x 1000

= 3892538925 x 10000

= 389250 38925 x 100000







7 0 6 4 2 0 9 0






706 4209000

706 420900000





706 4209000

0005961 asymp 596












= 34653465 divide 100 or 102

= 034653465 divide 1000 or 103

= 0034653465 divide 10000 or 104

= 0003465
















hundredth = 417











= 4 75100 = 4 325425 = 4 34Class Examples


























thousandth 36758





4290316290903

+ 650729

0000

206462759



= 23772Add 23037 + 167892



Add 605 + 12 + 0374 = 18424



















214x 036


7 704


Examples 920 x 37

= 34040000079 x 0025


870 x 46 = 40020

0000086 x 0057 = 0000004902



= 3892538925 x 100

= 3892538925 x 1000

= 3892538925 x 10000

= 389250 38925 x 100000







7 0 6 4 2 0 9 0






706 4209000

706 420900000





706 4209000

0005961 asymp 596












= 34653465 divide 100 or 102

= 034653465 divide 1000 or 103

= 0034653465 divide 10000 or 104

= 0003465
















hundredth = 417











= 4 75100 = 4 325425 = 4 34Class Examples

















thousandth 36758





4290316290903

+ 650729

0000

206462759



= 23772Add 23037 + 167892



Add 605 + 12 + 0374 = 18424



















214x 036


7 704


Examples 920 x 37

= 34040000079 x 0025


870 x 46 = 40020

0000086 x 0057 = 0000004902



= 3892538925 x 100

= 3892538925 x 1000

= 3892538925 x 10000

= 389250 38925 x 100000







7 0 6 4 2 0 9 0






706 4209000

706 420900000





706 4209000

0005961 asymp 596












= 34653465 divide 100 or 102

= 034653465 divide 1000 or 103

= 0034653465 divide 10000 or 104

= 0003465
















hundredth = 417











= 4 75100 = 4 325425 = 4 34Class Examples

















4290316290903

+ 650729

0000

206462759



= 23772Add 23037 + 167892



Add 605 + 12 + 0374 = 18424



















214x 036


7 704


Examples 920 x 37

= 34040000079 x 0025


870 x 46 = 40020

0000086 x 0057 = 0000004902



= 3892538925 x 100

= 3892538925 x 1000

= 3892538925 x 10000

= 389250 38925 x 100000







7 0 6 4 2 0 9 0






706 4209000

706 420900000





706 4209000

0005961 asymp 596












= 34653465 divide 100 or 102

= 034653465 divide 1000 or 103

= 0034653465 divide 10000 or 104

= 0003465
















hundredth = 417











= 4 75100 = 4 325425 = 4 34Class Examples















= 23772Add 23037 + 167892



Add 605 + 12 + 0374 = 18424



















214x 036


7 704


Examples 920 x 37

= 34040000079 x 0025


870 x 46 = 40020

0000086 x 0057 = 0000004902



= 3892538925 x 100

= 3892538925 x 1000

= 3892538925 x 10000

= 389250 38925 x 100000







7 0 6 4 2 0 9 0






706 4209000

706 420900000





706 4209000

0005961 asymp 596












= 34653465 divide 100 or 102

= 034653465 divide 1000 or 103

= 0034653465 divide 10000 or 104

= 0003465
















hundredth = 417











= 4 75100 = 4 325425 = 4 34Class Examples































214x 036


7 704


Examples 920 x 37

= 34040000079 x 0025


870 x 46 = 40020

0000086 x 0057 = 0000004902



= 3892538925 x 100

= 3892538925 x 1000

= 3892538925 x 10000

= 389250 38925 x 100000







7 0 6 4 2 0 9 0






706 4209000

706 420900000





706 4209000

0005961 asymp 596












= 34653465 divide 100 or 102

= 034653465 divide 1000 or 103

= 0034653465 divide 10000 or 104

= 0003465
















hundredth = 417











= 4 75100 = 4 325425 = 4 34Class Examples

























214x 036


7 704


Examples 920 x 37

= 34040000079 x 0025


870 x 46 = 40020

0000086 x 0057 = 0000004902



= 3892538925 x 100

= 3892538925 x 1000

= 3892538925 x 10000

= 389250 38925 x 100000







7 0 6 4 2 0 9 0






706 4209000

706 420900000





706 4209000

0005961 asymp 596












= 34653465 divide 100 or 102

= 034653465 divide 1000 or 103

= 0034653465 divide 10000 or 104

= 0003465
















hundredth = 417











= 4 75100 = 4 325425 = 4 34Class Examples


















214x 036


7 704


Examples 920 x 37

= 34040000079 x 0025


870 x 46 = 40020

0000086 x 0057 = 0000004902



= 3892538925 x 100

= 3892538925 x 1000

= 3892538925 x 10000

= 389250 38925 x 100000







7 0 6 4 2 0 9 0






706 4209000

706 420900000





706 4209000

0005961 asymp 596












= 34653465 divide 100 or 102

= 034653465 divide 1000 or 103

= 0034653465 divide 10000 or 104

= 0003465
















hundredth = 417











= 4 75100 = 4 325425 = 4 34Class Examples














Examples 920 x 37

= 34040000079 x 0025


870 x 46 = 40020

0000086 x 0057 = 0000004902



= 3892538925 x 100

= 3892538925 x 1000

= 3892538925 x 10000

= 389250 38925 x 100000







7 0 6 4 2 0 9 0






706 4209000

706 420900000





706 4209000

0005961 asymp 596












= 34653465 divide 100 or 102

= 034653465 divide 1000 or 103

= 0034653465 divide 10000 or 104

= 0003465
















hundredth = 417











= 4 75100 = 4 325425 = 4 34Class Examples















= 3892538925 x 100

= 3892538925 x 1000

= 3892538925 x 10000

= 389250 38925 x 100000







7 0 6 4 2 0 9 0






706 4209000

706 420900000





706 4209000

0005961 asymp 596












= 34653465 divide 100 or 102

= 034653465 divide 1000 or 103

= 0034653465 divide 10000 or 104

= 0003465
















hundredth = 417











= 4 75100 = 4 325425 = 4 34Class Examples


















7 0 6 4 2 0 9 0






706 4209000

706 420900000





706 4209000

0005961 asymp 596












= 34653465 divide 100 or 102

= 034653465 divide 1000 or 103

= 0034653465 divide 10000 or 104

= 0003465
















hundredth = 417











= 4 75100 = 4 325425 = 4 34Class Examples


















706 4209000

706 420900000





706 4209000

0005961 asymp 596












= 34653465 divide 100 or 102

= 034653465 divide 1000 or 103

= 0034653465 divide 10000 or 104

= 0003465
















hundredth = 417











= 4 75100 = 4 325425 = 4 34Class Examples

















706 4209000

0005961 asymp 596












= 34653465 divide 100 or 102

= 034653465 divide 1000 or 103

= 0034653465 divide 10000 or 104

= 0003465
















hundredth = 417











= 4 75100 = 4 325425 = 4 34Class Examples
























= 34653465 divide 100 or 102

= 034653465 divide 1000 or 103

= 0034653465 divide 10000 or 104

= 0003465
















hundredth = 417











= 4 75100 = 4 325425 = 4 34Class Examples



















= 34653465 divide 100 or 102

= 034653465 divide 1000 or 103

= 0034653465 divide 10000 or 104

= 0003465
















hundredth = 417











= 4 75100 = 4 325425 = 4 34Class Examples















= 34653465 divide 100 or 102

= 034653465 divide 1000 or 103

= 0034653465 divide 10000 or 104

= 0003465
















hundredth = 417











= 4 75100 = 4 325425 = 4 34Class Examples




























hundredth = 417











= 4 75100 = 4 325425 = 4 34Class Examples

























hundredth = 417











= 4 75100 = 4 325425 = 4 34Class Examples



















hundredth = 417











= 4 75100 = 4 325425 = 4 34Class Examples























= 4 75100 = 4 325425 = 4 34Class Examples
















= 4 75100 = 4 325425 = 4 34Class Examples



























Documents

Chapter 3 - Decimals Math Skills – Week 4. Outline Introduction to Decimals – Section 3.1 Addition of Decimals – Section 3.2 Subtraction of Decimals –