Place Value with Decimals

How do I know what kind of decimal it is? The name of a decimal is determined by the number of places to the right of the decimal point Number of Places Decimal Name Example 1 tenths 0.7 2 hundredths 0.05 3 thousandths 0.016

What are mixed decimals? Mixed decimals are numbers with both whole numbers and decimals The name of a whole number is determined by the number of places to the left of the decimal point In the number 128.765, 1 is in the hundreds place, 2 is in the tens place, 8 is in the ones place, 7 is in the tenths place, 6 is in the hundredths place, and 5 is in the thousandths place

How do you read decimals? To read a decimal correctly, first find the decimal point Whole numbers are to the left of the decimal point; any numbers to the right of a decimal point form a decimal fraction Say “and” for the decimal point The decimal 2164.511 is read as “two thousand, one hundred sixty-four and five hundred eleven thousandths”

Zeros after the decimal point Writing extra zeros after the decimal point does not change the value! The decimals 0.2, 0.20, and 0.200 are equivalent decimals

Exercise 1 Write the decimals. Five thousandths Ninety-four thousandths Three hundred thirty-six and sixty-nine hundredths

Exercise 2 Write each decimal in words. 7884.011 5592.4 4.203 612.250 10.44

Exercise 3 In what place (on the place value chart) is the underlined digit? Write the answer. 1.475 3.763 7780.215 412.407 902.103

Rounding Decimal Numbers

The rounding poem Find your number Look right next door 4 or less, just ignore 5 or more add one more!

What about decimal numbers The same rules (and poem) apply! Round 4.167 to the closest hundredths 4.167 Find your number Look right next door 4.17

Remember If you are asked to round to the nearest tenth…….your answer stops at the tenth place! Example: Round 42.73 to the closest tenth would be 42.7

Special Case! Rounding a 9 Round 2.197 to the closes hundredths Since there is a “9” in the hundredths place consider the tenth and hundredths together – 19 – do you leave it at 19 or move it to 20? 2.20 which is the same as 2.2

Round 4.95 to the closest tenth Since there is a “9” in the tenth spot consider the ones and tenths together…… should you leave it at 49 or move it to 50? 4.95 rounded to the nearest tenth is 5.0 which is equal to 5.

Try these 4.56 4.6 5.32 5.3 0.98 1.0 Round to hundredths Round to tenths: 4.56 4.6 18.784 18.78 5.32 5.3 9.46 9.456 10.00 0.98 1.0 9.997

Operations on Decimal Numbers

What You Will Learn: To add and subtract decimal numbers To multiply decimal numbers To use estimation to check your answers

Adding and Subtracting Decimals Before actually performing addition and subtraction of decimal values, we need to work on estimating Estimation provides us with a ‘ballpark’ figure so we can check our answer

Adding and Subtracting Decimals We use column addition and subtraction to add and subtract decimals The reason for this is so that we can align the decimal places

Ex: Add the following 3.2 + 6.8 4.51 + 1.76 c) 9.1 + 5.04

Ex: Subtract the following 8.57 – 3.12 4.07 – 2.64 10.3 – 7.06

Problem Solving Leslie has $5.50. She purchases some gum for $1.29 and an iced tea for $1.79. How much money does Leslie have left? 5.50 – 1.29 – 1.79 = ?

Multiplying Decimals When multiplying decimals, estimation can again be used to check our answer Ex: Chris finds 5 books at a cost of $1.65 each. He has $9.00 in change. Can he afford to buy these books?

Multiplying Decimals The process of multiplying decimals is no different from multiplying any other two numbers The number of decimal places in the final answer is equal to the number of decimal places that you start with.

Ex: Multiply the following 1.5 × 3 7.5 × 1.2 3.6 × 4.0

Problem Solving: Karl is preparing apple pies for a family reunion. He will need 5 pounds of apples to make the pies. Apples cost $1.29 / lb. What will the total cost of the apples be? 5(1.29) =

Examples: 5.3 × 1.2 + 4.5 4.6 + 1.6 x 2.4 + 5