OBJECTIVES Each student will be able to: 1-Make reasonable estimates adding, subtracting, multiplying or dividing with decimals. 2-Compare, add, subtract,

Complete

Decimals Review

OBJECTIVESEach student will be able to:

1-Make reasonable estimates adding, subtracting, multiplying

or dividing with decimals.

2-Compare, add, subtract, multiply and divide decimals.

A Terminating decimal, such as 0.75 has a finite number of decimal places.

A Repeating decimal, such as 0.666… has a block of one ore more digits that repeat continuously.

Key Vocabulary for this lesson

Key Vocabulary for this lesson

Base-10 system Is what we call our number system in which all numbers are expressed using the digits 0-9.

Place value refers to the value of a digit depending on its place in a number.

Examples: In 675 the value of ‘7’ is 70. In 723 the value of ‘7’ is 700.

Base 10 is what we call our number system.

In the Base 10 number system, all numbers are expressed using the digits 0-9.

Quick review…

In base 10:• The first number to the left of the

decimal point represents the number of 1's.

• The second number represents the number of 10's.

• The third number represents the number of 100's.

This is the place value system.

KEY CONCEPT!

As we move to the right, divide by 10.As we move to the left, multiply by 10.

55

The value of this 5 is ten times greater than the value of this 5.

Here are the place values:

As we move to the right, divide by 10. As we move to the left, multiply by 10.

We need to understand this to work with decimals.

___ , ___ ___ ___ .___ ___ ___Ones

Thousa

ndsHundredsTe

ns

Tenth

sHundredth

sTh

ousandth

s

This diagram shows the names of each place- including the first three decimal places. The decimal point separates values greater than one whole from those less than one whole.

Decimal point

Decimals To find the value of a decimal place,

we divide the value of the decimal place to the left of it by 10.

The sequence of numbers 1000, 100, 10, 1, continues to the left of the decimal point:   0.1 = 1/10

0.01 = 1/1000.001 = 1/1000

Quick review…

___,___ ___ _3_ ._3_ ___ ___

Ones

ThousandsHundredsTens

TenthsHundredthsThousandths

Decimal point

Divide the 3 in the Ones place by 10, and

you have the value of the 3 in the Tenths place. This pattern continues.

Guided Practice

REPRESENTING DECIMALS

The summer camp Jason attends is exactly four hundred twenty-three and four tenths miles from his home. Write four hundred twenty-three and four tenths in standard form.

REPRESENTING DECIMALS

BUILDING. When measuring board footage for some exotic woods, a carpenter must use 1.25 for thickness rather than 1 in her calculations. Write 1.25 in expanded form. 

REPRESENTING DECIMALS

CONSTRUCTION. Ella set out a board of pine lumber that was 0.8 feet long and a board of cedar lumber that was 0.80 feet long. Alberto said the cedar board was longer. Is he correct? Explain.

ORDERING DECMALS

CONSTRUCTION. Alberto is setting out four boards of lumber. The lengths of the boards are 4.5 feet, 4.52 feet, 4 feet, and 4.505 feet. Order the lengths from longest to shortest.

ROUNDING DECIMALS

SNOWBOARDING. Mike, Jake, and Aaron are buying snowboards. Mike is getting his snowboard on sale for $219.49. Jake’s costs $279.97. Aaron’s costs $234.95. Round each snowboard price to the nearest dollar.

ESTIMATING SUMS AND DIFFERENCES

BASKETBALL. Len dribbled a basketball for 43 seconds before Greg got the ball away. Then Greg dribbled the ball for 11.525 seconds before Len got the ball. Estimate how many more seconds Len dribbled the ball than Greg.

Key Point: When adding or subtracting decimals, be sure to line up the decimal points.

ADDING AND SUBTRACTING DECIMALS

MUSIC A piano solo on a CD is 5.33 minutes long. A guitar solo is 9.67 minutes long. How much longer is the guitar solo than the piano solo? First estimate the difference. Then find the actual difference.

Key Point:No need to line up the decimals points when you multiply. Just place the decimal point in the product when you are finished.

MULTIPLYING DECIMALS BY WHOLE NUMBERS

COOKING: Norberto uses three 14.7 oz. cans of chicken broth when he makes his delicious tortilla soup. How many total ounces of chicken broth does he use?

MULTIPLYING DECIMALS

Colin is filling 4.5 ounce bottles with lavender bubble bath that he made for gifts. He was able to fill 7.5 bottles. How many ounces of bubble bath did he make?

Key Point:When dividing, write a decimal point directly above the one in the dividend before you begin dividing.

Dividing Decimals by Whole Numbers

Frank, Gina, Judy, and Connie are splitting their dinner bill. After tip, the total is $30.08. How much does each owe if they split the bill four ways?

Key Point:If the divisor is a decimal number, make it into a whole number before you begin dividing.

DIVIDING BY DECIMALS

Nikki is buying some refrigerator magnets for her friends. Her total bill is $16.80. If magnets are $0.80 each, how many magnets is she buying?

Congratulations!

You have just learned everything there is to know about decimals.

ASSIGNMENTS

1. COMPLETE DECIMAL REVIEWWord Problem Practice

2. Go to the website for some fun math games.

http://www.math-play.com/decimal-math-games.html

Stare at the black dot...

After a while, the gray haze around it will appear to shrink.