Download RULES EXAMPLE PRACTICE Scientific Notation to Standard Form

SCIENTIFIC NOTATION – Notes (STUDENT)
Name: __________________
REVIEW:
8³ * 8¯⁶ = __________
7⁹ ÷ 7¯² = ___________
(4³)² = __________
(6¯³)⁴ = ______________
Standard Form – a number written in its _____________ form. (The ____________ you get when you solve a problem.)
Scientific Notation is a way to abbreviate very __________________ or very _________________ using powers of ____.
**First number is less than 10, but greater than or = to 1, and second number is a power of _______.
WHAT ARE WE
DOING???
RULES
1. if + exponent, move the
decimal to make the 1st
number ___________.
Scientific Notation
to
Standard Form
Standard Form
to
Scientific Notation
2. if a – exponent, move the
decimal to make the 1st
number ___________.
DECIMALS with ZEROS in front
(numbers less than 1 whole) =
negative exponents
1. Move the decimal point
shown until you get BEHIND
the first non-zero digit.
(This makes a new decimal,
*less than 10, and ≥ 1.)
2. Now count how many
places the decimal point
was moved. (Put that as
your negative exponent as
a power of 10)
WHOLE #’s & Decimals ≥ 1 =
positive exponents
1. For Whole #s, place a
decimal BEHIND the
number and move the
decimal until only 1 nonzero digit is in front of the
decimal.
2. For Decimals ≥ 1, just move
the decimal shown until
only 1 digit is in front of the
decimal.
3. Now count how many times
you moved your decimal.
(put that as your +
exponent of 10)
EXAMPLE
PRACTICE
3.12 x 10⁶
4.17 x 10⁴
1.35 x 10¯⁴
3.9 x 10¯³
0.000057
0.00000045
0.0000003
0.0004
307,000
0.000457
460,100,000
0.0000789
6,980,000
6,500,000
I. Practice: Put the following in Standard Notation: (Remember, + exp., # gets bigger, - exp., # gets smaller)
a) 3.12 x 109
f) 8.2 x 106
b) 4.275 x 102
g) 8.2 x 10
c) 1.35 x 10
-6
h) 4.49 x 105
-4
d) 4.7 x 107
i) 7.4 x 101
e) 2.395 x 10
j) 2.6 x 102
-3
k) 7.113 x 10
-3
II. Write in Scientific Notation: (Remember, if # in standard form is < 1, we use – exp., if # > 1, we use + exp.)
a) 345,000
b) 62,000,000,000
c) 1,000,000
e) 0.00004
f) 0.000000086
g) 0.25
*d) 345.25
h) 42,050
i) .0005
III. Put the following in Standard Form:
a) 6.23 x 104
b) 1.99 x 10
e) 3.114 x 107
f) 2.4 x 10
-4
c) 1.5 x 10
-1
-3
d) 7.5 x 104
g) 1.4 x 1011
h) 6.2 x 10
-8
IV. Put the following in Scientific Notation:
a) 59, 740,000
f) 0.000000037
b) 2,300
g) 10,000,000
c) 0.000068
h) 41, 351
d) 0.004
e) 36
i) 0.569
SCIENTIFIC NOTATION – Notes (TEACHER)
REVIEW:
8³ * 8¯⁶ = __________
7⁹ ÷ 7¯² = ___________
Name: ________________
(4³)² = __________
(6¯³)⁴ = ______________
Standard Form – a number written in its original form. (The answer you get when you solve a problem.)
Scientific Notation is a way to abbreviate very large numbers or very small numbers using powers of 10.
**First number is less than 10, but greater than or = to 1, and second number is a power of __10_____.
RULES
1. if + exponent, move the
decimal to make the 1st
number _BIGGER__.
Scientific Notation
to
Standard Form
Standard Form
to
Scientific Notation
2. if a – exponent, move
the decimal to make the
1st number _SMALLER__.
DECIMALS with ZEROS in front
(numbers less than 1 whole) =
negative exponents
1. Move the decimal point
until you get BEHIND
the first non-zero digit.
(This makes a new
decimal, *less than 10,
and ≥ 1.)
2. Now count how many
places the decimal point
was moved. (Put that
as your - exponent as
a power of 10)
WHOLE #’s & Decimals ≥ 1 =
positive exponents
1. For Whole #s, place a
decimal BEHIND the
number and move the
decimal until only 1 nonzero digit is in front of
the decimal.
2. For Decimals ≥ 1, just
move the decimal
shown until only 1 digit
is in front of the
decimal.
3. Now count how many
times you moved your
decimal. (put that as
your + exponent of 10)
EXAMPLE
3.12 x 10⁶
3,120,000
PRACTICE
4.17 x 10⁴
41,700
1.35 x 10¯⁴
0.000135
3.9 x 10¯³
0.0039
0.000057
5.7 x 10¯⁵
0.00000045
4.5 x 10¯⁷
0.0000003
3.0 x 10¯⁷
0.0004
4.0 x 10¯⁴
307,000
3.07 x 10⁵
0.000457
4.57 x 10¯⁴
460,100,000
4.601 x 10⁸
0.0000789
7.89 x 10¯⁵
6,980,000
6.98 x 10⁶
6,500,000
6.5 x 10⁶
I. Practice: Put the following in Standard Notation: (Remember, + exp., # gets bigger, - exp., # gets smaller)
a) 3.12 x 109
a) 3,120,000,000
f) 8.2 x 106
-3
c) 1.35 x 10
d) 4.7 x 107
e) 2.395 x 10
b) 427.5
c) .000135
d) 47,000,000
e) 0.002395
g) 8.2 x 10
f) 8,200,000
-4
b) 4.275 x 102
-6
h) 4.49 x 105
i) 7.4 x 101
h) 449,000
i) 74
g) .0000082
j) 2.6 x 102
k) 7.113 x 10
j) 260
-3
k) 0.007113
II. Write in Scientific Notation: (Remember, if # in standard form is < 1, we use – exp., if # > 1, we use + exp.)
a) 345,000
b) 62,000,000,000
a.) 3.45 x 106
e) 0.00004
e) 4 x 10
b) 6.2 x 1010
f) 8.6 x 10
*d) 345.25
c) 1 x 106
f) 0.000000086
-5
c) 1,000,000
d) 3.4525 x 102
g) 0.25
-8
h) 42,050
g) 2.5 x 10
-1
i) .0005
h) 4.205 x 104
i) 5 x 10
-4
III. Put the following in Standard Form:
a) 6.23 x 104
a) 62,300
e) 3.114 x 107
e) 31, 140,000
b) 1.99 x 10
-4
c) 1.5 x 10
b) 0.000199
f) 2.4 x 10
-1
f) 0.24
-3
d) 7.5 x 104
c) 0.0015
d) 75,000
g) 1.4 x 1011
h) 6.2 x 10
g) 140,000,000,000
-8
h) 0.000000062
IV. Put the following in Scientific Notation:
a) 59, 740,000
a) 5.974 x 107
f) 0.000000037
f) 3.7 x 10
-8
b) 2,300
b) 2.3 x 103
g) 10,000,000
g) 1 x 107
c) 0.000068
d) 0.004
c) 6.8 x 10
-5
d) 4 x 10
h) 41, 351
h) 4.1351 x 104
e) 36
-3
e) 3.6 x 101
i) 0.569
i) 5.69 x 10
-1