using exponents to write large numbers june 25, 2012
DESCRIPTION
Objectives Write numerals in exponential form Write numerals in exponential form Express in standard form the numerals in exponential form or expanded exponential form or vice versa Express in standard form the numerals in exponential form or expanded exponential form or vice versaTRANSCRIPT
Using Exponents to WriteLarge Numbers
June 25, 2012June 25, 2012
For Learning to Happen!
•Clear your desk of anything that may distract you.
•Remove all other thoughts from your mind.
•Pay close attention.•Try all the examples.•Ignore all other distractions.
ObjectivesWrite numerals in exponential Write numerals in exponential
formformExpress in standard form the Express in standard form the
numerals in exponential form or numerals in exponential form or expanded exponential form or expanded exponential form or vice versavice versa
Exponents of TenWhat Is the Standard Form What Is the Standard Form
of These Tens?of These Tens?
210101010
345
1001,00010,000100,000
Exponents of TenNotice that the number of zerosNotice that the number of zerosmatches the exponent numbermatches the exponent number
210101010
345
1001,00010,000100,000
Multiplying Multiples of Ten
Multiply These NumbersMultiply These Numbers
100 x 2 =1,000 x 3 =10,000 x 7 =100,000 x 9 =
2003,00070,000900,000
Multiplying Multiples of TenDid you notice that all you Did you notice that all you
have to do is multiply 1 x wholehave to do is multiply 1 x wholenumber & add the zeros behind?number & add the zeros behind?
100 x 2 =1,000 x 3 =10,000 x 7 =100,000 x 9 =
2003,000
70,000900,000
Short Cut for Writing Large Numbers
Combine these two steps forCombine these two steps forwriting large numbers.writing large numbers.
6 x 10 2 =6 x (10 x 10) = 6 x 100 = 600
600
Short Cut for Writing Large Numbers
Remember!Remember!The exponent is the same as the The exponent is the same as the
number of zeros.number of zeros.
6 x 10 2 = 600
What is the Standard Number?
7 x 10 2 = 700
What is the Standard Number?
8 x 10 3 = 8,000
What is the Standard Number?
9 x 10 4 = 90,000
What is the Standard Number?
4 x 10 2 = 400
What is the Standard Number?
13 x 10 2 = 1 300
What is the Standard Number?
216 x 10 1 = 2 160
What is the Exponent Form?
5 x 10 2
=500
What is the Exponent Form?
6 x 10 3
=6,000
What is the Exponent Form?
9 x 10 4
=90,000
What is the Exponent Form?
7 x 10 5
=700,000
What is the Exponent Form?
65 x 10 4
=650,000
What is the Exponent Form?
107 x 10 3
=107,000
The human eye blinks about once every The human eye blinks about once every five seconds. In 16 waking hours, an five seconds. In 16 waking hours, an average person blinks about 11 500average person blinks about 11 500times a day or 4 200 000 times a year.times a day or 4 200 000 times a year.
Study how each numeral is written in Study how each numeral is written in Expanded exponential form in 3 ways.Expanded exponential form in 3 ways.
1. Giving the value of each digit1. Giving the value of each digit
2. Multiply each digit by its place value2. Multiply each digit by its place value
3. Multiply each digit by powers of 103. Multiply each digit by powers of 10
11 500
Study how each numeral is written in
Expanded exponential form in 3 ways.
10 000 + 5001 000 +
+
1 x 10 000 ++ 1 x 1 000
5 x 100
(1 x 104)
(1 x 103)
(5 x 102)
+
1. Giving the value of each digit1. Giving the value of each digit
2. Multiply each digit by its place value2. Multiply each digit by its place value
3. Multiply each digit by powers of 103. Multiply each digit by powers of 10
Expanded Exponential Form of 23 400Expanded Exponential Form of 23 400
23 400
20 000 + 4003 000 +
+
2 x 10 000 ++ 3 x 1 000
4 x 100
(2 x 104)
(3 x 103)
(4 x 102)
+
(2 x 104)
+ (3 x 103)
+ (4 x 102)
Exponential Form of 23 400?
234 x 102
1. Giving the value of each digit1. Giving the value of each digit
2. Multiply each digit by its place value2. Multiply each digit by its place value
3. Multiply each digit by powers of 103. Multiply each digit by powers of 10
Expanded Exponential Form of 6 052Expanded Exponential Form of 6 052
6 052
6 000 + 250 +
+
6 x 1 000 ++ 5 x 10 2 x 1
(6 x 103)
(5 x 101)
(2 x 100)
+
(6 x 103)
+ (5 x 101)
+ (2 x 100)