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New Jersey Center for Teaching and Learning

Progressive Mathematics Initiative

http://www.njctl.org/


5th Grade

Decimal Concepts

www.njctl.org

2013-06-19




Setting the PowerPoint ViewUse Normal View for the Interactive ElementsTo use the interactive elements in this presentation, do not select the Slide Show view. Instead, select Normal view and follow these steps to set the view as large as possible:

• On the View menu, select Normal.

• Close the Slides tab on the left.

• In the upper right corner next to the Help button, click the ^ to minimize the ribbon at the top of the screen.

• On the View menu, confirm that Ruler is deselected.

• On the View tab, click Fit to Window.

Use Slide Show View to Administer Assessment ItemsTo administer the numbered assessment items in this presentation, use the Slide Show view. (See Slide 13 for an example.)

Define and Review Vocabulary

Identify Place Values

Read and Write Decimals

Compare and Order Decimals

Round Numbers to Designated Place Values

Table of Contents

Click on a topicto go to that section.

Define and Review Vocabulary

Return to Table of Contents

A Decimal Number (based on the number 10) contains a Decimal Point.

Click to find out!

What is a decimal number?

Blue BlockRed Block

How many yellow rods are needed to fill the blue block? 10

Yellow Rod

How many red blocks are needed to fill the blue block? 100(Hint: Fill a yellow rod with red blocks)

What is the value of a red block? one-hundredth (0.01)

One Unit (1)

click

What is the value of a yellow rod? one-tenth (0.1)click

click

click

Blue = One Unit

3 yellow blocks = 0.3three tenths

23 red blocks = 0.23twenty three hundredths

Blue = One Unit

Interactive Number Grid - Use to Show DecimalsClick to Go to Interactive Site

http://www.apples4theteacher.com/math/games/blank-100-number-chart.html

http://www.apples4theteacher.com/math/games/blank-100-number-chart.html

1 If the square equals one whole, what does the shaded area represent?





Identify Place Values


Place Value

As you look at the place value chart, how many times does the value of the number increase as you go to the left?

Each place has a value that is 10 times the value of its place to the right.

click for answer

Place Value

As you look at the place value chart, how many times does the value of the number increase as you go to the right?

Each place has a value that is ten times smaller than the value of its place to its left.

click for answer

Place Value Chart

6 What digit is in the hundreds place?

987,654.0123

6

2

1

A

B

C

D 7

7

7

2

3

A

B

C

D 8

What digit is in the thousandths place? 987,654.0123

8 What digit is in the tenths place?

987,654.0123

1

4

0

A

B

C

D 5

9 What digit is in the ten thousands place?

987,654.0123

3

7

4

A

B

C

D 8

10 What digit is in the hundredths place?

987,654.0123

5

0

1

A

B

C

D 2

Decimals on the number line

2 3

What does each line represent on this number line between the whole numbers of 2 and 3?Label the number line.


32 33

What does each line represent on this number line between the whole numbers of 32 and 33?Label the number line.


4.3 4.4

What does each line represent on this number line between the decimal numbers of 4.3 and 4.4?Label the number line.


0.63

0.64

What does each line represent on this number line between the decimal numbers of 0.63 and 0.64?Label the number line.

Decimal Number Lines Tool

Click for instructions and to use the tool.

http://www.mathsonline.co.uk/freesite_tour/resource/whiteboard/decimals/dec_notes.html





National Library of Virtual ManipulativesClick to go to web site.

Change Places to "Decimals"

at the bottom left.

Zoom in to drag the dot

more precisely.

http://nlvm.usu.edu/en/nav/frames_asid_334_g_2_t_1.html?from=category_g_2_t_1.html

11 Where would the number 4.4 go on this number line?

A B C D0 10


A B C D0 10


A B C D0 1


A B C D7 8


A B C D19 20


A B C D

324

325


A B C D5.3 5.4


A B C

D Not on this number line

1 1.1


A B C6.2 6.3



A B C17.1 17.2


Read and Write Decimals


Remember the place values after the decimal point start with tenths

mill

ion

hu

nd

red

th

ou

san

dte

n t

ho

usa

nd

tho

usa

nd

hu

nd

red

ten

on

e

and

ten

th

hu

nd

red

thth

ou

san

dth

ten

th

ou

san

dth

9, 8 7 5, 6 1 0 . 4 7 9

This number is read:

Nine million, eight hundred seventy-five thousand, six hundred ten AND four hundred seventy-nine thousandths

0 . 0 7

5 4 6 . 2 5 9

8 . 3

0 . 8 9

0 . 0 1 1

2 3 5 4 . 6

9 . 7

Can you read the number?th

ou

san

ds

hu

nd

red

s

ten

s

on

es

and

ten

ths

hu

nd

red

ths

tho

usa

nd

ths

×

6.16

0.052

2,104.371

6.371

0.03

645.16

2,104.03

0.004

403.5

83,042.004

Read the following numbers.

1. Look to see if there is a number to the left of the decimal; if so write it out. If there is no number to the left of the decimal, skip to step 3. 2. Write an and for the decimal point. 3. Write the number in the decimal part. 4. Write the word for the place value of the rightmost digit.

How do you write a decimal in words?

Write 13.24 in words

Thirteen and twenty-four hundredthsclick

How does a comma help when writing a decimal number?

The place value before the comma is always stated.

For example:

1,547 is writtenOne THOUSAND, five hundred forty-seven

6,547,100 is written6 MILLION, five hundred forty-seven THOUSAND, one hundred

×

Write the decimal in words

1) 5.04 Five and four hundredths

2) 146.457 One hundred forty-six and four hundred fifty-seven thousandths

3) .0009 Nine ten-thousandths

4) 6,345.149 Six thousand, three hundred forty-five and one hundred forty-nine thousandths

Match each number and written form.

four thousand fifty three

four hundred five and three tenths

forty and fifty three hundredths

four thousand and fifty three

four and fifty three thousandths

forty and fifty three hundredths

405.3

4.53

40.53

none

4.053

4,053

21 What is 4.36 in written form?

four and thirty six

four and thirty six tenths

four, thirty six

A

B

C

D four and thirty six hundreths


sixty three and sixty seven hundredths

sixty three and sixty seven thousandths

sixty three and sixty seven

A

B

C

D sixty three, sixty seven thousandths


zero and four hundred nineteen

four hundred nineteen hundredths

four hundred nineteen thousandts

A

B

C

D four one nine


nine and nine

nine hundredths

nine and nine hundredths

A

B

C

D nine and zero nine tenths


four zero seven zero two one

nine and nine tenths

four hundred seven and twenty one thousandths

A

B

C

D four hundred seven and twenty one hundredths

Writing a decimal numerically

1. If there is a ths, there will be a decimal

2. If there is an and, there will be a whole number to the left of the decimal

3. Note the ending - this is the place where the decimal number will end

4. Use the decimal chart to help you!

×

Use the chart as a guide to write the decimal numbers

1. two hundred sixteen and 2 tenths

2. thirty two and nine thousandths

3. four thousand, five hundred six and twenty four hundredths

4. nine hundred and eight hundredths

tho

usa

nd

s

hu

nd

red

s

ten

s

on

es

and

ten

ths

hu

nd

red

ths

tho

usa

nd

ths

26 What is fifty two and eighteen hundredths?

52,18

52.01852.18

A

B

C

D 52.0018

27 What is five thousand fifty and five hundredths?

550.5

5,050.5

5,050.05

A

B

C

D 5,500.05

28 What is six hundred three and four thousandths?

603.4

603.004

603.04

A

B

C

D 603.0004

29 What is thirty four hundredths?

340

34

0.34

A

B

C

D 0.034

30 What is four hundred ninety five thousandths?

495

495.000

0.0495

A

B

C

D 0.495

Compare and Order Decimals


There are two symbols we use to compare numbers.

> (greater than)

< (less than)

One number goes on the left of the symbol and another number goes on the right of the symbol.

The number on the left of the ">" shows the larger number. For example: 2 > 1

The number on the left of the "<" shows the smaller number.For example: 1 < 2

Symbols and Words to remember when comparing numbers

>

<

=

greater than/largest

less than/ smallest

equal

SYMBOL WORDS

Comparing Decimals

• Line up the decimal points• Put zeros in wherever digits are missing• Compare the digits, from left to right• The largest digit, having the same place value, names the

largest number

0.0450.210

Compare 0.045 and 0.21

• Line up the decimal points• Put zeros in wherever digits are missing• Compare the digits, from left to right• The largest digit, having the same place

value, names the largest number

put zero on the

end

Compare left to right. 2 is greater than 0, so 0.21 is

greatest.

0.045 < 0.21Click

0.3600.312




put zero on the

end

Compare left to right. 6 is greater than 1, so 0.36 is greatest.

0.36 > 0.312Click

0.0090.020




put zero on the

end

Compare left to right. 2 is greater than 0, so 0.02 is greatest.

0.009 < 0.02Click

Decimal Squares Interactive GamesClick for link.

Game could also be played with two students having a spinner and writing down

their decimal number.

In this game the robot won because 0.7950 is greater

than 0.5021

http://www.decimalsquares.com/dsGames/



31 Choose the correct symbol.

0.41 0.049>

<

=

A

B

C


0.301 0.311>

<

=

A

B

C


0.007 0.05>

<

=

A

B

C


0.179 0.24>

<

=

A

B

C


0.46 0.6>

<

=

A

B

C

Ordering Decimals

• Line up all of the decimal points• Put zeros in wherever digits are missing• Compare the digits, from left to right• The largest digit, having the same place value, names the largest number

Example:

910.800085.007910.801911.900085.070

What digit tells us this is the largest number?

1

Why isthis the smallest number?

Compare the digitsClick

×

36 The number with the least value is:

61.005

61.3

61.05

A

B

C

D 61.04

37 The number with the least value is:

0.005

0.5

0.05

A

B

C

D 0.0005

38 The number with the greatest value is:

9.888

9.8

9.008

A

B

C

D 9.088

39 The number with the greatest value is:

0.67

0.067

0.0067

A

B

C

D 0.00067

40 How much money would you like to win?

$150.59

$140.99

$150.82

A

B

C

D $140.50

Rewrite the numbers to order them from least to greatest.

15, 0, 1.5, 0.015, 0.15

0.709, 0.009, 0.68, 0.08, 0.07

Rewrite the numbers to order them from least to greatest.

41 Which of the following is ordered least to greatest?

0.3, 0.03, 0.33, 3.3

0.03, 0.3, 0.33, 3.3

3.3, 0.33, 0.3, 0.03

A

B

C


0.008, 0.06, 0.5

0.5, 0.06, 0.008

0.06, 0.5, 0.008

A

B

C

43 Which of the following is ordered greatest to least?

8.07, 0.008, 0.087, 0.87

0.008, 0.087, 0.87, 8.07

8.07, 0.87, 0.087, 0.008

A

B

C

44 Which of the following is ordered greatest to least?

0.23, 0.08, 0.009

0.23, 0.009, 0.08

0.009, 0.08, 0.23

A

B

C


0.8, 0.32, 0.41, 0.701

0.8, 0.701, 0.41, 0.32

0.32, 0.41, 0.701, 0.8

A

B

C

Round Numbers to Designated Place

ValuesReturn to Table of Contents

Rounding makes numbers that are easier to work with in your head.

• Rounded numbers are only approximate.• An exact answer generally can not be obtained using

rounded numbers.• Use rounding to get an answer that is close but that does

not have to be exact.

1. Put your pencil point under the digit in the tens place.

Look to the right.

2. Is the digit 5 or more?

Yes OR No

3. What happens to the digit?

Increases by 1 OR remains the same

4. What happens to everything to the left of the tens place?

Those digits always remain the same.

5. What happens to everything to the right of the tens place?

Those digits become zero.

Round 8,749 to the nearest ten.Review

1. Put your pencil point under the digit in the hundreds place.

Look to the right.


Yes OR No



4. What happens to everything to the left of the hundreds place?


5. What happens to everything to the right of the hundreds place?

Those digits become zero.

Round 8,749 to the nearest hundred.Review

46 Round 143 to the nearest ten

47 Round 4,561 to the nearest hundred.

48 Round 564,012 to the nearest hundred thousand.

49 Round 7,399 to the nearest thousand.


What happens in this case?

Round 697 to the nearest ten.

The 7 to the right of the 9 tells us to increase the 9 by 1.

What happens?

Answer ____________


52 Round 98 to the nearest ten.

53 Round 399,238 to the nearest ten thousand.

54 Round 9,521 to the nearest thousand.


Let's learn how to round decimals using the following examples:

Round 687.268 to the nearest tenths place.

When rounding decimals, put your pencil point under the place value that you are rounding to

DO NOT MOVE IT

687.268

Rounding Decimals

1. Put your pencil point under the digit in the tenths place.

Look to the right.


Yes OR No



4. What happens to everything to the left of the tenths place?


687.268

5. What happened to the digits to the right of the tenths place?

Remember, we are rounding.

The place values to the right of the tenths place have zero value, so now the digits 6 and 8 become zeroes.

687.300 = 687.3

However we leave the zeros off when they are to the right of the decimal point.

1. Put your pencil point under the digit in the hundredths place.

Look to the right.

2. Is the digit 5 or more? Yes OR No

3. What happens to the digit? Increases by 1 OR remains the same

4. What happens to everything to the left of the hundredths place?


5. What happens to everything to the right of the hundredths place?

Those digits become zero (and we leave them off since they are to the right of the decimal).

Round 8.73258 to the hundredths place.

Try this:Round 687.4953 to the nearest hundredths place

Answer: 687.50click

56 Round

6874.6479

to the nearest hundredth.

57 Round

6874.6479

to the nearest ten.

58 Round

6874.6479

to the nearest hundred.

59 Round

6874.6479

to the nearest tenth.

60 Round

6874.6479

to the nearest thousand.

61 Round

6874.6479

to the nearest thousandth.

When rounding to a specific place, your answer MUST have a digit in that place.

Example:Round 23.97 to the nearest tenth

Answer: 24.0There must be a digit in the tenths place, since we were to round to the tenths place.

Caution!

62 Round

678.97


63 Round

6.304

to the nearest hundredth.

64 Round

5.03


65 Round

0.3497

to the nearest thousandth.

66 Round

84.951


Use rounding to estimate answers to problems.

At a restaurant, a burger is $5.99, fries are $3.85 and a small drink is $1.29. Round to the nearest dollar to estimate the cost to purchase all three items.

Cost Estimate$5.99 $6$3.85 $4$1.29 $1

It would cost about $11 to purchase all three items.

67 Round the following items to the nearest dollar to figure out the approximate cost if all the items were bought.

pens $2.99pencils $2.20book bag $15.75


jeans $24.99t-shirt $6.79hat $12.31


milk $3.79bread $2.15juice $2.40

70 Round the following items to the nearest half dollar to figure out the approximate cost if all the items were bought.

chicken $8.60potatoes $2.45peas $0.99

71 Round the following items to the nearest half dollar to figure out the cost if all the items were bought.

apples $4.60bananas $1.90oranges $3.10

72 Round the following items to the nearest ten dollars to figure out the approximate cost if all the items were bought.

sneakers $36.21sweatshirt $13.99socks $6.00

73 Round the following items to the nearest hundred dollars to figure out the approximate cost if all the items were bought.

computer $688.23printer $213.50desk $175.89

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