Scientific Notation
A short-hand way of writinglarge numbers without writing all of the zeros.
The Distance From the Sun to the Earth
93,000,000 miles
Step 1
Move decimal left
Leave only one significant number in front of the decimal
Step 2
Write number without zeros
Step 3
Count how many places you moved decimalMake that your power of tenThe power of ten is the letter “E” (exponential) for your calculators.
The power often is 7 becausethe decimalmoved 7 places.
93,000,000 - Standard Form
9.3 x 107 - Scientific Notation
4567 x 10-5 -
Scientific Notation
.04567 -
Standard Form
What if it has a decimal?
Move the decimal to the right after the first significant (not a zero) number.
.000,000,043 --- Standard Form
4.3 x 10-8 - Scientific Notation
Practice Problems
1.) 9.85 x 10-4? =
2.) 64,100,000,000 =
3.) 2.79 x 10-6 =
4.) 431,200,000 =
5.) .000,0496=
1) .000,985
2) 6.41 x1010
3) .000,00279
4) 4.31 x 108
5) 4.96 x 10-5
Write in scientific notation or standard form.
More Practice Problems
1) 734,000,000 = ______ x 108
2) .000,000,000,870 = ______x 10-10
3) 90,000,000,000 = _____ x 1010
On these, decide where the decimal will be moved.
1)7.34 x 108
2) 8.70 x 10-103) 9.0 x 1010
Complete Practice Problems
1) 50,000
2) 7,200,000
3) .000,000,802
Write in scientific notation .
1) 5.0 x 1042) 7.2 x 106 3) 8.02 x 10-7
Scientific Notation to Standard Form
Move the decimal to the right
3.4 x 105 in scientific notation
340,000 in standard form
3.40000 --- move the decimal
Write in Standard Form
6.27 x 106
9.01 x 104
4.603 x 108
9.94 x 102
6,270,000
90,100
460,300,000
994
Write in Scientific Notation
3.89 x 10-7
3.872 x 10-6
8.940 x 10-3
4.931 x 10-3
23.8761 x 10-4
.000,000,389
.000,003,872
.00894
.004931
.00238761
Write in Scientific Notation1. 0.07882 =2. 0.000,00272338 =3. 118000 =4. 87200 =5. 0.000,02786 =6. 0.000,000664 =7. 450 =8. 74171.7 =9. 770 =10. 0.000,0085 =
1. 7.882 × 10-2
2. 2.72338 × 10-63. 1.18 × 105
4. 8.72 × 104
5. 2.786 × 10-5
6. 6.64 × 10-7
7. 4.5 × 102
8. 7.41717 × 104
9. 7.7 × 102
10. 8.5 × 10-6
1. What is this number in standard form? 6.73 x 10-6
6730
000
.000
0067
3
.000
0673
6730
00
0% 0%
50%50%A. 6,730,000
B. 0.00000673
C. 0.0000673
D. 673,000
2. When the exponent is positive you move the decimal to the:
Lef
t
Rig
ht T
op
botto
m
11%6%
0%
83%A. Left
B. Right
C. Top
D. bottom
3. What does your calculator use to designate as a power of ten for scientific notation
10 P G E
11%
78%
11%
0%
A. 10
B. P
C. G
D. E
4. Why is scientific notation important when dealing with astronomy?
They
wan
t to
They
are
real
l...
Pla
nets
and s
t...
It h
elps
with
...
0%7%
80%
13%
A. They want to
B. They are really big numbers and they are lazy
C. Planets and stars are really far away so using scientific notation makes it easier to record the numbers
D. It helps with Inverse Square Law
5. Which of these numbers shows 1 million in scientific notation?
1 x
103
1 x
104
1 x
107
1 x
106
0%
56%
44%
0%
A. 1 x 103
B. 1 x 104
C. 1 x 107
D. 1 x 106
6. Changer 1204.6 in scientific notation?
1.2
x 1
03
120
x 1
0-2
12
x 10
2
120
4 x
100
79%
14%7%
0%
A. 1.2 x 103
B. 120 x 10-2
C. 12 x 102
D. 1204 x 100
7. Change 17.8 in scientific notation?
1.7
8 x
102
1.7
8 x
101
1.7
8 x
10-1
1.7
8 x
10-2
17%
0%
11%
72%A. 1.78 x 102
B. 1.78 x 101
C. 1.78 x 10-1
D. 1.78 x 10-2
8. Change 567,310 in scientific notation?
567
x 1
03
56.
7 x
105
5.6
7310
x 1
05
5 x
106
22%
0%
67%
11%
A. 567 x 103
B. 56.7 x 105
C. 5.67310 x 105
D. 5 x 106
9. Convert 8.36 x 102 in scientific notation?
8360
083
60 836
8360
00
17%
0%
78%
6%
A. 83600
B. 8360
C. 836
D. 836000
10. Convert 9.16 x 106 in scientific notation?
.000
0009
16
.000
916
9160
9160
000
6%
94%
0%0%
A. 0.000000916
B. 0.000916
C. 9,160
D. 9,160,000