8–3
Scientific Notation
SOL A.10 The student will apply the laws of exponents to perform operations on
expressions with integral exponents, using scientific notation when appropriate.
EXAMPLE
Scientific to Standard Notation
⫺3
WHAT YOU’LL LEARN
a. Express 7.48 ⫻ 10
• Express numbers in
7.48 10
scientific notation and
standard notation.
3
in standard notation.
0.00748
n 3 move decimal point
places to the
.
• Find products and
quotients of numbers
expressed in scientific
notation.
5
b. Express 2.19 ⫻ 10 in standard notation.
5
2.19 10 219000
n
move decimal point
places to the
.
Your Turn Express each number in standard notation.
KEY CONCEPT
2
a. 3.16 10
3
Scientific Notation A
number is expressed in
scientific notation when
it is written as a product
of a factor and a power
of 10. The factor must
be greater than or equal
to 1 and less then 10.
b. 7.61 10
EXAMPLE
Standard to Scientific Notation
a. Express 0.000000672 in scientific notation.
0.000000672
n
0.000000672 10
Move decimal point
places to the
right.
0.000000672 a
and
© Glencoe/McGraw-Hill
n
b. Express 3,022,000,000,000 in scientific notation.
3,022,000,000,000
n
3,022,000,000,000 10
Move decimal point
places to the
3,022,000,000,000 a
.
and
n
Glencoe Algebra 1
183
8–3
REMEMBER IT
Count decimal places
carefully when
converting numbers
between scientific and
standard notation.
Your Turn Express each number in scientific notation
a. 458,000,000
b. 0.0000452
EXAMPLE
Multiplication with Scientific Notation
Evaluate. Express each result in scientific and standard
notation.
6
(7 10
12
)(4.3 10 )
6
(7 4.3)(10
12
10 )
6
30.1 10
Commutative and
Association Properties
Product of
1
6
(3.01 10 ) 10
30.1 Property
7
3.01 10 or
EXAMPLE
Product of
Division with Scientific Notation
6.4 ⴛ 104
1.6 ⴛ 10
Evaluate ᎏᎏ7 .
6.4 104
1.6 107
冢 冣冢 冣
0000
0000
0000
0000
4 10
or
Associative Property
Product of
3
5
a. (3 10 )(2.1 10
HOMEWORK
ASSIGNMENT
Page(s):
Exercises:
184
Glencoe Algebra 1
1.36 10
b. 4
7
2.5 10
)
© Glencoe/McGraw-Hill
Your Turn Evaluate. Express each result in scientific
and standard notation.