Engrade › Wikis › Decimals - Unit 2: Cluster 3

Decimals are used to help us write numbers that are smaller than one. Decimal points are used to represent values that are less than one. Numbers to the left of a decimal point represent whole numbers, and numbers to the right of the decimal point represent parts of a whole number. Decimals can also be represented as fractions and percents. [b]Example:[/b] 27% = 27/100 = 0.27

What Are Decimals?

{http://s3.amazonaws.com/engrade-myfiles/4052559855671367/decimals.gif}

Decimal Examples

{http://s3.amazonaws.com/engrade-myfiles/4056575515597034/decimals01-3.gif}

Decimal Examples

{http://s3.amazonaws.com/engrade-myfiles/4058079791967119/ExplNumb.gif}

Decimal Examples

Steps for Rounding Decimals Step 1: Go the place value that you are being asked to round to. Step 2: If the digit to the right of the place you are round to is 4 or less, round down. If the digit to the right of the place you are round to is 5 or greater, round up. Step 3:Drop the rest of the digits after the place you rounded to. [b]Examples:[/b] Round 8.65 to the nearest tenth. 8.7 Round 23.60556 to the nearest tenth. 23.6 Round 6.6793 to the nearest hundredth. 6.6 Round 98.1048 to the nearest hundredth. 98.10

Rounding Decimals

[http://teachertube.com/viewVideo.php?video_id=115531&title=Rounding_Decimals]

Rounding Decimals Video

Step 1: Write the problem vertically, with the decimal points lined up. Step 2: Add any extra zeros if needed. Step 3: Add/Subtract. Step 4: Place the decimal point in the answer, lined up under the other decimal points.

Adding & Subtracting Decimals

Multiplying Decimals: Step 1: Multiply the numbers without their decimal points. Step 2: Count the number of decimal places in each factor and add those numbers. Step 3: Place the decimal point in the product, based on the number of spaces you added in step 2. Count from the right in your product. Step 4: Add any zeros needed as you are adding the decimal point. Dividing Decimals By Whole Numbers: Step 1: Place the decimal point for the quotient directly above the decimal point in the dividend. Step 2: Solve the problem as if you were dividing whole numbers. Dividing Decimals By Decimals: Step 1: Change the divisor to w whole number by moving the decimal point as many places as necessary to the right. Step 2: Move the decimal point in the dividend the same number of places to the right. Step 3: Place the decimal in the quotient. Step 4: Divide as you would divide whole numbers.

Multiplying & Dividing Decimals

[http://teachertube.com/viewVideo.php?video_id=126187]

Multiplying & Dividing Decimals Video #1

[http://teachertube.com/viewVideo.php?title=Multiplying_and_Dividing_Decimals&video_id=130016]

Multiplying & Dividing Decimals Video #2

How do we compare decimals? Step 1: Line up the decimal points. Step 2: Begin at the left. Find the first place where the digits are different. Step 3: Compare the decimals using <, >, or =. [b]Example:[/b] The Castillo de Marcos National Monument in Florida is on 20.51 acres. The Gettysburg National Cemetery in Pennsylvania is on 20.58 acres. Which national landmark is on more land? 20.51 20.58 .51 < .58 [b]Answer:[/b] The Gettysburg National Cemetery is on more land. [b]Example:[/b] What symbol makes this sentence true? 0.286__________0.268 0.286 0.268 [b]Answer:[/b] .28 > .26 so 0.286 > 0.268 How do we order decimals? Step 1: Line up the decimal points. Step 2: Begin at the left. Find the first place where the digits are different. Step 3: Compare the remaining digits. [b]Example:[/b] During the softball season, Leah’s batting average was 0.322, Emily’s average was 0.224, and Erika’s average was 0.314. Order the averages form greatest to least. 0.322 0.224 0.314 0.322 > 0.314 > 0.224 [b]Answer:[/b] So the averages in order from greatest to least are: Leah, Erika, Emily [b]Example:[/b] Order these decimals from least to greatest. 9.42 3.218 4.08 11.262 9.42 3.218 4.08 11.62 [b]Answer:[/b] 11.62 is the greatest because it has the biggest whole number part. 9.42 is the second greatest because it has the second biggest whole number part. 4.08 is the third greatest because it has the third biggest whole number part. 3.218 is the smallest because it has the smallest whole number part. 3.218 4.08 9.42 11.62

Comparing & Ordering Decimals

Why are estimating decimals useful? In real life, knowing how to estimate answers involving decimals is a useful skill. It is particularly useful when you need to estimate how much money you need to buy several items or how much change you should get back. How do we estimate the sums, differences, products, ad quotients of decimals? [b]Example:[/b] Nick earns $203.80 each day he works. About how much does he earn in a 5-day week? Step 1: Which operations should you use? The question asks how much he earns in 5 days. Since he earns the same amount each day, you can multiply to solve the problem. Step 2: Round $203.80 to the nearest ten dollars. The digit to the right of the tens place is 3: Round down to $200. Step 3: Multiply the rounded amount by the number of days. 5 x 200 = 1,000 [b]Answer:[/b] Nick earns about $1,000 in a 5-day week [b]Example:[/b] Kayleigh had two bags of potatoes. The first bag weighed 8.25 kl. The second bag weighed 7.73 kl. Estimate to the nearest whole number, the total weight of the two bags of potatoes. Step 1: Which operation should you use? The question asks for the total weight of the two bags. Since each bag weighs a different amount, you should add the amounts to find the total. Step 2: Round the decimals. 8.25 rounded to the nearest whole number is 8. 7.73 rounded to the nearest whole number is 8. Step 3: Add the rounded numbers. 8 + 8 = 16 [b]Answer:[/b] A good estimate of the total weight of the two bags is 16 kilograms. [b]Example:[/b] Eleven people had lunch in a restaurant. With tax and tip, the total came to $95.60. If the divided the check evenly, about how much will each person pay? [b]Math Alert:[/b] When you need to estimate a quotient, using rounded numbers is not always the best idea. Instead use compatible numbers. Compatible numbers are numbers that are close to the given numbers, and are easy to divide mentally. Step 1: Which operation should you use? Since the total cost is being divided evenly between 11 people, division should be used. Step 2: Choose compatible numbers that are easy to divide. $95.60 is close in value to $96. 11 will not divide $96 evenly, but 11 will divide $99 evenly. So, divide 99 by 11 to estimate the quotient. Step 3: Divide the compatible numbers. 99 ÷ 11 = 9 [b]Answer:[/b] Each person will pay about $9.

Estimating With Decimals