Transcript Exponents PowerPoint

Todays outcomes are:
A1 – model and use power, base and exponents to
reporesent repeated multiplication
A2 – Rename numbers among exponential, standard
and expanded forms.
There are many different ways to
show multiplication
7
x 7 x 7 x7
 (7)(7)(7)(7)
7
·7·7·7
Exponents
 Exponents
are the mathematician’s
shorthand for writing multiplication.
7
· 7 · 7 · 7 is the same as writing 74
since there are four 7’s being
multiplied together.
 Likewise, (5)(5)(5) is the same as
writing 53 since there are three 5’s
being multiplied together.
The format for exponents is:
(base)exponent
The exponent tells you how many of the
base are being multiplied together.
Example:
43 = 4 · 4 · 4 = 64
More about exponents
 If
you are asked to put something into
exponential form then your answer
should have a base and an exponent.
 Example: write 5 · 5 · 5 in exponential form.
Answer: 53
 If
you are asked to put something into
standard form your answer should show
no exponents.

Example: write 64 in standard form.
Answer: 1296
Examples: Try these
yes that means write them down and answer them!!! 
1.
2.
3.
4.
5.
6.
What is the base in each of the following powers?
a) 32
b) 16
c) 79
What is the exponent in each of these powers.
a) 24
b) 518
c) 110
Write these numbers in exponential form:
a) 2 · 2 · 2
b) 4 · 4
c) 8 · 8 · 8 · 8
Write these numbers in expanded form:
a) 32
b) 16
c) 79
Evaluate these powers:
a) 92
b) 17
c) 53
Write each power in exponential form using the indicated base:
a) 16 as a power of 2
b) 1000 as a power of 10
c) 81 as a power of 3
d) 625 as a power of 5
The answers:
1.
2.
3.
4.
5.
6.
a) 3
b) 1
c) 7
a) 4
b) 18
c) 0
Write these numbers in exponential form:
a) 23
b) 42
c) 84
Write these numbers in expanded form:
a) 3 · 3
b) 1 · 1 · 1 · 1 · 1 · 1
c) 7 · 7 · 7 · 7 · 7 · 7 · 7 · 7 · 7
Evaluate these powers:
a) 81 b) 1
c) 125
Write each power in exponential form using the
indicated base:
a) 24
b) 103
c) 34
d) 54
Place Value Review
7 8 9
.
1 2 3 4 5 6
thousandths
hundredths
tenths
decimal point
ones
tens
hundreds
thousands
ten thousands
hundred thousands
Rounding review
the steps and rules for rounding
numbers
 Step
1: identify the number in the place
you are being asked to round to.
 Step 2: Look at the number to the right of
that number
• Rule 1: if the number to the right is a 5 or larger
then increase your original number by 1
• Rule 2: if the number to the right is a 4 or lower
then the original number stays the same
 Step
3: change all the digits to the right
into zeros.
Examples: Try these
yes that means write them down and answer them!!! 
1.
2.
3.
In the number 1 876 345.920 which digit is in
the following place?
a) ones ___
b)hundredths ____
c) millions ___ d)thousands ____
In the number 472 985.136 what is the place
value of:
a) 8 __________ b) 4 ___________
c) 1 __________ d) 9 ___________
Round 349 251 to the:
a) tens place ___________
b) thousands place __________
c) hundreds place ___________
Answers
1.
2.
3.
a) 5
b)2
c) 1
a) tens
b) hundred thousands
c) tenths
d) hundreds
a) 349 250
b) 349 000
c) 349 300
d)6
Expanded Notation of Whole
Numbers

Expanded notation is a way of writing a number
as the some of the values of its’ digits.

Example #1:
• Standard form: 372
• Expanded Form: (3 x 100) + (7 x 10) + (2 x 1)

Example #2
• Standard form: 52 908
• Expanded form:
(5 x 10 000) + (2 x 1000) + (9 x 100) + (0 x 10) + (8 x 1)