Download Guided Notes and Study Guide SCIENTIFIC NOTATION 1.) Defining

Guided Notes and Study Guide
SCIENTIFIC NOTATION
1.) Defining scientific notation:
A number written in scientific notation is a
number greater than or
equal to
but less than
multiplied by a power of
. Scientific notation
is written as
, where 1 < a < 10.
Ex. 1:
Ex. 2:
Ex. 3:
Ex 4:
2.45 x 108
0.0543 x 104
3 x 10-5
21.3 x 10-6
in scientific notation.
in scientific notation.
in scientific notation.
in scientific notation.
2.) Scientific to Standard Notation:
STEP 1: Determine whether the power of 10 is
or
.
 If the power of 10 is
, move the decimal that many units to the
.
 If the power of 10 is
, move the decimal that many units to the
.
STEP 2: Add in any
and
that are needed to indicate place
value.
Ex. 1:
Ex. 2:
2.45 x 108 =
3 x 10-5 =
The power of 10 is . It is
so I will
move the decimal point
places to the
. I will add zeros and commas.
The power of 10 is
. It is
so I will move the decimal point
to the
. I will add zeros.
places
3.) Standard to Scientific Notation:
STEP 1: Move the decimal so the number is greater than or equal to but less than .
STEP 2: Count the number of decimal places moved in STEP 1.
 If the decimal point was moved to the
or the original number was
, the count is
.
 If the decimal point was moved to the
or the original number was
, the count is
.
STEP 3: Write as a product of the
(found in STEP 1) and
raised
n
to the power of the count from STEP 2(in the form a x 10 ).
Ex. 1:
Ex. 2:
30,500,000  3.0500000 x 10n=
I moved the decimal point
the
, so the count is
a=
and n =
0.000781  00007.81 x 10n =
I moved the decimal point
the
, so the count is
a=
and n =
places to
.
.
places to
.
.
4.) Multiplication with Scientific Notation:
To multiply numbers in scientific notation, (1)
the numbers; (2)
the exponents; (3) multiply the product from STEP 1 by 10n, where n is the sum from STEP
2; and (4) rewrite the answer in correct scientific notation form (the first number must
be greater than or equal to
but less than
).
Ex:
Evaluate:
(5 x 10-8)(2.9 x 102)
= (5 x 2.9)(10-8 x 102)
= 14.5 x 10-8 + 2 = 14.5 x 10-6
= (1.45 x 101) x 10-6
= 1.45 x (101 x 10-6)
= 1.45 x (101+(-6))
= 1.45 x 10-5 or 0.0000145
Combine like terms.
Multiply numbers& add exponents.
14.5 = 1.45 x 101.
Combine like terms.
Add exponents.
Scientific &standard notation.
5.) Division with Scientific Notation:
To divide numbers in scientific notation, (1)
the numbers; (2)
the exponents; (3) multiply the quotient from STEP 1 by 10n, where n is the difference
from STEP 2; (4) rewrite the answer in correct scientific notion form (the first number
must be greater than or equal to
but less than
).
Ex:
Evaluate:
= 1.2789 109
5.22 105
= 0.245 x 104
1.2789 x 109
5.22 x 105
= (2.45 x 10-1) x 104
= 2.45 x (10-1 x 104)
= 2.45 x 10(-1)+4
= 2.45 x 103 or 2450
Combine like terms.
Multiply numbers & subtract
exponents.
0.245 = 2.45 x 10-1
Combine like terms.
Add exponents.
Scientific & standard notation.
Guided Notes and Study Guide
SCIENTIFIC NOTATION
1.) Defining scientific notation:
A number written in scientific notation is a decimal
number greater than or
equal to 1
but less than 10
multiplied by a power of 10 . Scientific notation
is written as a x 10n , where 1 < a < 10.
Ex. 1:
Ex. 2:
Ex. 3:
Ex 4:
2.45 x 108
0.0543 x 104
3 x 10-5
21.3 x 10-6
is
in scientific notation.
is not in scientific notation.
is
in scientific notation.
is not in scientific notation.
2.) Scientific to Standard Notation:
STEP 1: Determine whether the power of 10 is positive
or negative
.
 If the power of 10 is positive
, move the decimal that many units to the right .
 If the power of 10 is negative
, move the decimal that many units to the left.
STEP 2: Add in any zeros and commas
that are needed to indicate place value.
Ex. 1:
2.45 x 108 = 245,000,000
The power of 10 is 8 . It is positive
so
Iwill move the decimal point 8
places to the
right. I will add zeros and commas.
Ex. 2:
3 x 10-5 = 0.00003
The power of 10 is -5
. It is negative so I
will move the decimal point 5
places to the
left . I will add zeros.
3.) Standard to Scientific Notation:
STEP 1: Move the decimal so the number is greater than or equal to 1 but less than 10.
STEP 2: Count the number of decimal places moved in STEP 1.
 If the decimal point was moved to the left
or the original number was
greater than one, the count is positive
.
 If the decimal point was moved to the right
or the original number was less
than one, the count is negative
.
STEP 3: Write as a product of the number
(found in STEP 1) and 10
raised
n
to the power of the count from STEP 2(in the form a x 10 ).
Ex. 1:
30,500,000  3.0500000 x 10n= 3.05 x 107
I moved the decimal point 7
places to
the left
, so the count is positive.
a = 3.05
and n = 7
.
Ex. 2:
0.000781  00007.81 x 10n = 7.81 x 10-4
I moved the decimal point 4
places to
the right
,so the count is negative .
a = 7.81
and n = -4
.
4.) Multiplication with Scientific Notation:
To multiply numbers in scientific notation, (1) multiply
the numbers; (2) add
the exponents; (3) multiply the product from STEP 1 by 10n, where n is the sum from STEP
2; and (4) rewrite the answer in correct scientific notation form (the first number must
be greater than or equal to 1
but less than 10
).
Ex:
Evaluate:
(5 x 10-8)(2.9 x 102)
= (5 x 2.9)(10-8 x 102)
= 14.5 x 10-8 + 2 = 14.5 x 10-6
= (1.45 x 101) x 10-6
= 1.45 x (101 x 10-6)
= 1.45 x (101+(-6))
= 1.45 x 10-5 or 0.0000145
Combine like terms.
Multiply numbers& add exponents.
14.5 = 1.45 x 101.
Combine like terms.
Add exponents.
Scientific &standard notation.
5.) Division with Scientific Notation:
To divide numbers in scientific notation, (1) divide
the numbers; (2) subtract
the exponents; (3) multiply the quotient from STEP 1 by 10n, where n is the difference
from STEP 2; (4) rewrite the answer in correct scientific notion form (the first number
must be greater than or equal to 1
but less than 10
).
Ex:
Evaluate:
= 1.2789 109
5.22 105
= 0.245 x 104
1.2789 x 109
5.22 x 105
= (2.45 x 10-1) x 104
= 2.45 x (10-1 x 104)
= 2.45 x 10(-1)+4
= 2.45 x 103 or 2450
Combine like terms.
Multiply numbers & subtract
exponents.
0.245 = 2.45 x 10-1
Combine like terms.
Add exponents.
Scientific & standard notation.