Decimal Basics Powerpoint.ppt

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BASE 10 NUMBER SYSTEM

PLACE VALUE

READING DECIMALS

WRITING DECIMALS

COMPARE/ORDER DECIMALS

ROUNDING DECIMALS

Decimal

Basics

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What Are Decimals

 _{Like fractions, decimals are part of a whole.}

 Decimals show amounts between two consecutive

counting numbers (3,4…)

0.45 is between 0 and 1

3.861 is between 3 and 4

25,196.8 is between 25,196 and 25,197

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Understanding the Base 10

System

 _{Can you think of a number that doesn’t use the digits}

0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 in it?

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Base 10 Number System

 Our everyday number system is a Base-10 system.  The Base-10 number system is known as the decimal

system and has 10 digits to show all numbers (0,1,2,3,4,5,6,7,8,9)

 Numbers in this system are represented by using place

value and a decimal point to separate whole numbers from decimal fractions.

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Place Value in the Base 10

System

10 times larger 10 times smaller

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Digits to the Left are 10

times Bigger

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Digits to the Right are 10

times Smaller

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Place Value

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Place Value

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Place Value Charts

 _{A place value chart helps us read and write very large (or very small}

numbers)

 _{A decimal separates the whole numbers from the decimal numbers.}  _{To the left of the decimal (where the whole numbers are represented),}

the place value chart is divided into periods: ones, thousands, millions, billions, etc…

 _{Each period has 3 digits: a ones, tens, hundreds}

 _{So if you can read/write 3 digit combinations, you can read/write very}

large/small numbers.

H T O H T O H T O H T O

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Practice These 3 Digit

Combos

A

B

C

D

E

1

324

700

530

310

821

2

618

036

030

206

930

3

805

912

006

076

090

4

401

018

000

015

800

5

695

130

990

001

007

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Decimal Values End in “th”

With the exception of the ones, places to the right have the same names but

the end in “th” or “ths”

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How do I know what kind of

decimal it is?

 _{The name of a whole number is determined by the}

number of places to the left of the decimal point

 _{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

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Identify the Place Value of a Digit

Identifying the Place Value of

Digits

2 3 . 6 4 3

0 . 9 8 5

Tenths or 6 tenths

Thousandths or 5

thousandths

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Identify the Place Value

Practice

 _{What place is the 4 in the number 12.}₄₅₆  _{What place is the 2 in the number 156.8}₂₇₈  _{What place is the 7 in the number 5}₇_.894  _{What place is the 8 in the number 615.65}₈₃  _{What place is the 1 in the number 5}₁_3.987  _{What place is the 5 in the number 1.678}₅

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Identify the Place Value

Practice

 _{What place is the 4 in the number 12.}₄₅₆

 Tenths

 _{What place is the 2 in the number 156.8}₂₇₈

 Hundredths

 _{What place is the 7 in the number 5}₇_.894

 Ones

 _{What place is the 8 in the number 615.65}₈₃

 Thousandths

 What place is the 1 in the number 513.987

 Tens

 _{What place is the 5 in the number 1.678}₅

 Ten Thousandths

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Decimals in Different

Forms

Standard Form Word Form Expanded Form

3.19 Three and nineteen hundredths 3 + 0.1 + 0.09 2.813 Two and eight-hundred thirteen

thousandths

2 + 0.8 + 0.01 + 0.003

42.5301 Forty-two and five thousand three-hundred one

ten-thousandths

40 + 2 + 0.5 + 0.03 + 0.0001

 _{There are 3 forms of every decimal #}

 Standard Form

 Word Form

 Expanded Form

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Reading Decimals

 _{Say what you see before the decimal}  Say “and” for the decimal

 _{Say what you see after the decimal}  _{Say the place value of the final digit}

Example:

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Reading Decimals

Examples:

_{0.043 is read as 43 thousandths} _{0.65 is read as 65 hundredths}

_{6.00072 is read as 6 and 72 hundred-thousandths}

Putting the numbers in

a place value chart might help.

0 . 0 4 3 0 . 6 5

6 . 0 0 0 7 2

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Reading Decimals – Your

Turn

Use a place value chart to read the following:

22.789 _17.54

_1,456.009 245.00087

_{17,124,397.00902}

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Reading Decimals – Your

Turn

Use a place value chart to read the following: _22.789

 Twenty-two and seven hundred eighty-nine thousandths

_17.54

 Seventeen and fifty-four hundredths

1,456.0009

 One-thousand four-hundred fifty six and nine ten-thousandths

_245.00087

 Two-hundred forty-five and eighty-seven hundred-thousandths

_{17,124,397.000902}

 Seventeen million, one-hundred twenty-four thousand, three-hundred

ninety-seven and nine-hundred two millionths

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Writing Decimal Numbers

Using a place value chart will help

1.Write the whole number

o Insert each 3 digit combo into the correct period on a place value chart

if necessary

o Remember to use a comma between each period

2.Listen for the word “and” to place the decimal point. 3.Write the part to the right of the decimal

o Listen for the # after “and”

o Listen for the place value. On the place value chart, put a dash in the

final position.

o Write the number you heard, ending at the last dash. o Fill in any empty dashes with zeros.

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Writing Decimal Numbers

 _{Fourteen and three tenths = 14.3}

 _{Three thousand one and ninety three thousandths}= 0.093

 _{Four and seventy ten-thousandths = 4.0070}

1 4 . 3

3, 0 0 1 . 0 9 3

4 . 0 0 7 0

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Writing Decimal – Your Turn

Use a place value chart to write the following:

Two thousand six and four hundredths

_{Five hundred eighty-one and sixty ten-thousandths} _{Twelve-thousand four and twenty-one millionths}

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Writing Decimal – Your Turn

Use a place value chart to write the following:

Two thousand six and four hundredths

 2,006.04

_{Five hundred eighty-one and sixty ten-thousandths}

 581.0060

Twelve-thousand four and twenty-one millionths

 12,004.000021

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Equivalent Decimals

 _{Equivalent means “equal”}

 Adding zeros to the left of the whole # does not

change the value

 Example: 2.1 = 02.1 = 002.1 = 0002.1

 Writing extra zeros after the decimal point does not

change the value!

 The decimals 0.2, 0.20, and 0.200 are equivalent decimals

=

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Comparing Decimals

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Compare/Order Decimals

2 3 5

4 1

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Rounding Decimals



When rounding decimals it is first necessary to

identify the place value you are rounding to.



The digit that follows will tell you whether you

should round up or leave the digit the same.



If the digit is:

 5 or higher – round up by one

 4 or lower – leave the same



Digits past the rounded digit are not recorded

in the rounded number.

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Rounding Tips

 Circle the place value you are rounding to.

 Underline the digit that follows; it is this digit that tells you to round up or leave the same.

 Example:

 34.561 rounded to the nearest tenth is . . .

3 4 . 5 6 1

34.6

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Rounding – Additional

Examples

 4.6341 rounded to the nearest hundredth is . . .

 4. 6 3 4 1 = 4.64

 67.1125 rounded to the nearest thousandths is

 67. 1 1 2 5 = 67.113

 .6971 rounded to the nearest hundredth is . . .

 . 6 9 7 1 = 0.70 (since the 9 needs to be rounded up to 10,

this carries to the next digit left)

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HERE ARE SOME PRACTICE PROBLEMS IN WHICH I WILL WORK THROUGH WITH YOU TO MAKE

SURE THAT YOU UNDERSTAND THE MAIN CONCEPTS COVERED.

Practice

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Exercise 1

In 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

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Exercise 2

Write the decimals in standard form (with #s)

1.Five thousandths

2.Ninety-four thousandths

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

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Exercise 3

Write each decimal in words.

1.7884.011 2.5592.4 3.4.203 4.612.250 5.10.44

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Exercise 4

Write a decimal that has the same number.

1.0.2 2.5.51 3.410.6 4.753.809

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Exercise 5

 _{Order the following from least to greatest using the}

stacking method

