Decimals Math 6

Decimal Basics Decimals

Decimal Basics Watch Brain Pop: Decimals http://www.brainpop.com/math/numbersandoper ations/decimals/

Decimal Basics How much of $1.00 does a Loonie represent? 1 whole of a dollar 1/1 1.00

One Whole

Decimal Basics Whole Numbers on a Number Line

Decimal Basics How much of $1.00 does a dime represent? 1 tenth of a dollar 1/10 0.1

Decimal Basics A whole separated into tenths

Decimal Basics

Decimal Basics

Decimal Basics Comparison

Decimal Basics How much of $1.00 does a penny represent? 1 hundredth of a dollar 1/100 0.01

A whole separated into hundredths

Decimal Basics

Decimal Basics Hundredths on a Number Line

Decimal Basics Comparison of tenths and hundredths

Decimal Basics

Decimal Basics How much of $1.00 does a nickel represent? 5 hundredth of a dollar 5/100 0.05

Decimal Basics

Decimal Basics Fifths on a Number Line

Decimal Basics How much of $1.00 does a quarter represent? 25 hundredth of a dollar 25/100 0.25

Decimal Basics

Decimal Basics Twenty-fifths on a Number Line

Decimal Basics A whole separated into thousandths

Decimal Basics

Decimal Basics

Decimal Basics

Decimal Basics

Decimal Basics

Decimal Basics 3.268 579 = three AND two hundred sixty-eight thousandths, five hundred seventy-nine millionths 3 . 2 6 8 5 7 9 ones and 10ths 100ths 1000ths 10,000ths 100, 000ths 1000,000ths

Decimal Basics Key Points Represents less than one whole number As we move right (on a PVC), each position is 10 times smaller There is NO oneths spot (on a PVC) Are “read” in the same way as whole numbers

Decimals and Fractions

Decimal & Fractions BIG IDEA Decimals and Fractions are different ways of showing the same value

Decimal & Fractions A fraction is a part of a whole We call the top number the Numerator, it is the number of parts you have We call the bottom number the Denominator, it is the number of parts the whole is divided into

Decimal & Fractions Decimal Fraction 0.01 1/100 0.05 5/100 0.1 10/100 0.25 25/100 0.5 50/100 0.75 75/100 0.8 80/100 0.9 90/100 0.99 99/100

Decimal & Fractions Use your calculator The easiest way to convert a fraction to a decimal is to divide the top number by the bottom number divide the numerator by the denominator in mathematical language 63/100 = 0.63

Multiplying Decimals by Whole Numbers

Multiplying Decimals by Whole Numbers What you know When whole numbers are multiplied the product is always greater Ex. 5 x 10 = 50

Multiplying Decimals by Whole Numbers Do you see a pattern in the table? 0.2658 x 1  =  0.2658 0.2658 x 10 2.658 0.2658 x 100 26.58 0.2658 x 1,000 265.8 0.2658 x 10,000 2,658. 0.2658 x 100,000 26,580. 0.2658 x 1,000,000 265,800.

Multiplying Decimals by Whole Numbers In the Table the decimal 0.2658 is being multiplied by multiples of 10. (10, 100, 1000, 10,000) Each time we multiply by a multiples of 10, the decimal point is moved one place to the right. When decimals are multiplied by multiples of 10, the product is greater than the decimal being multiplied Ex. 2.8 x 10 = 28

Multiplying Decimals by Whole Numbers Rule: For every 0 the decimal shifts one spot to the right

Multiplying Decimals by Whole Numbers An electrician earns $18.75 per hour. If he worked 200 hours this month, then how much did he earn?

Multiplying Decimals by Whole Numbers METHOD 1 – The decimal is greater than one Step 1: Estimate $18.75 -> 20.00 $20 x 200 = $4000 Your solution should be around $4000

Multiplying Decimals by Whole Numbers METHOD 1 – The decimal is greater than one Step 2: Multiply Multiply the numbers as if they were whole numbers (remove the decimal) 1875 x 200 = 375000

Multiplying Decimals by Whole Numbers METHOD 1 – The decimal is greater than one Step 3: Replace the decimal Use the estimate ($4000) replace the decimal to around decimal amount 3750.00

Multiplying Decimals by Whole Numbers The electrician earned $3750.00 for the month

Multiplying Decimals by Whole Numbers TRY THESE – Use all 3 steps to solve 2 x 1.43 2 x 5.34 6 x 3.95

Multiplying Decimals by Whole Numbers Stefan drinks a glass of pure orange juice each morning. The Orange Juice contains 0.054g of Vitamin C per glass. How much Vitamin C does Stefan get from orange juice each week?

Multiplying Decimals by Whole Numbers METHOD 2 – The decimal is less than one Step 1: Remove the decimal (Jump Out) 0.054 00.54 005.4 54.

Multiplying Decimals by Whole Numbers METHOD 2 – The decimal is less than one Step 2: Multiply Multiply the numbers as if they were whole numbers 54 x 7 = 378

Multiplying Decimals by Whole Numbers METHOD 2 – The decimal is less than one Step 3: Replace the decimal (Jump In) 378. 37.8 3.78 0.378

Multiplying Decimals by Whole Numbers Stefan receives 0.378gof Vitamin C from Orange juice each week.

Multiplying Decimals by Whole Numbers TRY THESE – Use all 3 steps to solve 2 x 0.243 4 x 0.034 6 x 0.0051

Multiplying Decimals by Whole Numbers

Multiplying Decimals by Whole Numbers Project Preview: Determine the amount of each base ten block

1.0

0.1

Multiplying Decimals by Whole Numbers Project Preview 0.01

Multiplying Decimals by Whole Numbers Project Preview

Multiplying Decimals by Whole Numbers Project Preview Using the image as a guide, try to model the following decimal 2.23

Multiplying Decimals by Whole Numbers

Multiplying Decimals by Whole Numbers Project Preview Using the image as a guide, try to model the following decimal multiplication 1.35 x 4 = 5.4

Multiplying Decimals by Whole Numbers

Dividing Decimals by Whole Numbers Decimals, Fractions, Percent

Dividing Decimals by Whole Numbers What you know When whole numbers are divided the quotient is always less Ex. 50 ÷ 10 = 5

Dividing Decimals by Whole Numbers Do you see a pattern in the table? 3526.58 ÷ 1  =  3526.58 3526.58 ÷10 352.658 3526.58 ÷ 100 35.2658 3526.58 ÷ 1,000 3.52658 3526.58 ÷ 10,000 0.352658 3526.58 ÷ 100,000 0.0352658 3526.58 ÷ 1,000,000 0.00352658

Dividing Decimals by Whole Numbers In the Table the decimal 3526.58 is being divided by multiples of 10. (10, 100, 1000, 10,000) Each time we divided by a multiple of 10, the decimal point is moved one place to the left. When decimals are divided by multiples of 10, the quotient is less than the decimal being divided Ex. 2.8 ÷ 10 = 0.28

Dividing Decimals by Whole Numbers Rule: For every 0 the decimal shifts one spot to the left

Dividing Decimals by Whole Numbers There are three types of decimals:

Dividing Decimals by Whole Numbers Terminating decimals stop at some point (aka rational) 5.649375 0.125 3.75 2.125

Dividing Decimals by Whole Numbers Repeating decimals repeat forever, but there is a pattern to their repetition 5. 333333333333 / 5.3 0. 363636363636 / 0.36 1.83444444 / 1.834

Dividing Decimals by Whole Numbers Non-recurring decimals are decimals that go on forever, but there is no pattern 3.1415926535897932384626433832795028841971693993751 05820974944592307816406286…

Dividing Decimals by Whole Numbers There are NO remainders when dividing decimals

Dividing Decimals by Whole Numbers Using LONG DIVISION to divide decimals 9.45 ÷ 4 4 9.45

Dividing Decimals by Whole Numbers Using LONG DIVISION to divide decimals 10.4 ÷ 3 3 10.4

Dividing Decimals by Whole Numbers Using LONG DIVISION to divide decimals 3.1 ÷ 7 7 3.1

Dividing Decimals by Whole Numbers Often a decimal umber needs to be rounded. There are several factors to consider: Money is ALWAYS rounded to the nearest 100th Are there instructions? (Round to the nearest thousandth) What are you measuring? (Kilometers, inches, Litres) General rule is 2-3 decimal spots

Dividing Decimals by Whole Numbers Rochelle entered 3 frogs into the Frog Olympics. The total distance the frogs travelled was 4.92m. About how far did each frog travel?

Dividing Decimals by Whole Numbers METHOD 1 – The decimal is greater than one Step 1: Estimate Think… the number needs to be a multiple of 3 4.92 -> 6 (or 3) 6 ÷ 3 = 2 Your solution should be around 2

Dividing Decimals by Whole Numbers METHOD 1 – The decimal is greater than one Step 2: Divide Divide the numbers as if they were whole numbers (remove the decimal) 492 ÷ 3 = 164

Dividing Decimals by Whole Numbers METHOD 1 – The decimal is greater than one Step 3: Replace the decimal Use the estimate from step 1 (2) replace the decimal 1.64

Dividing Decimals by Whole Numbers Each frog traveled about 1.64m

Dividing Decimals by Whole Numbers TRY THESE – Use all 3 steps to solve 16.64 ÷ 4 9.45 ÷ 5 62.8 ÷ 8

Dividing Decimals by Whole Numbers Quincy has 0.926m of string. Suppose he cuts the string into 4 equal lengths. What is the length of each piece of string?

Dividing Decimals by Whole Numbers METHOD 2 – The decimal is less than one Step 1: Remove the decimal (Jump Out) 0.9 2 6 09. 2 6 09 2 . 6 09 2 6.