Place Value with DecimalsPlace 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 1Write the decimals.

1.Five thousandths

2.Ninety-four thousandths

3.Three hundred thirty-six and sixty-nine hundredths

Exercise 2Write each decimal in words.

1.7884.011

2.5592.4

3.4.203

4.612.250

5.10.44

Exercise 3In what place (on the place value chart) is the

underlined digit? Write the answer.

1.1.475

2.3.763

3.7780.215

4.412.407

5.902.103

Rounding Decimal NumbersRounding Decimal Numbers

The rounding poemThe rounding poem

Find your number

Look right next door

4 or less, just ignore

5 or more add one more!

What about decimal numbersThe same rules (and poem) apply!

Round 4.167 to the closest hundredths

4.167 Find your number

Look right next door

4.174.17

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 42.742.7

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 2.22.2

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 55.

Try these

Round to tenths:

4.56 4.6

5.32 5.3

0.98 1.0

Round to hundredths

18.784 18.78

9.456 9.46

9.997 10.00

Operations on Decimal NumbersOperations 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 DecimalsAdding 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

a) 3.2 + 6.8

b) 4.51 + 1.76

c) 9.1 + 5.04

• Ex: Subtract the following

a) 8.57 – 3.12

b) 4.07 – 2.64

c) 10.3 – 7.06

Problem SolvingProblem 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 DecimalsMultiplying 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 equalequal to the number of decimal places that you start with.

Ex: Multiply the following a) 1.5 × 3

b) 7.5 × 1.2

c) 3.6 × 4.0

Problem Solving: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:Examples:

a) 5.3 × 1.2 + 4.5

b) 4.6 + 1.6 x 2.4 + 5