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P-___ Sci – SCIENTIFIC NOTATION
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SCIENTIFIC NOTATION  is a system of writing NUMBERS with a LARGE number
Of place value positions often held by ZEROES
A. SCIENTIFIC NOTATION is a NUMBER written as a product with two FACTORS
1. The 1st FACTOR is a single digit whole number greater than 0, but less than 10
2. The 2nd FACTOR is a POWER of 10 in exponential form
B. Steps for writing a standard NUMBER in SCIENTIFIC NOTATION format:
1. Move the decimal POINT until the first NUMBER is between 1-10, but not 10
2. Count the number of PLACE VALUE positions moved and express that total as
an EXPONENT
a. When you move the DECIMAL point to the left, the EXPONENT will be
expressed as a positive number
b. When you move the DECIMAL point to the RIGHT, the EXPONENT
will be expressed as a NEGATIVE number
c. (e.g.) 100,000 = 1 x 105
0.0000004 = 4 x 10 -7
150,000,000 = 1.5 x 108
0.00000634 = 6.34 x 10 -6
d. (e.g.) There are 2 sextillion OXYGEN [O] atoms in a drop of water and
4 sextillion HYDROGEN [H] atoms.
1. Scientific notation: oxygen atoms 2,000,000,000,000,000,000,000 = 2 x 1021
hydrogen atoms 4,000,000,000,000,000,000,000 = 4 x 1021
e. (e.g.) There are 1 quintillion ATOMS that make up one dot of ink on a
newspaper
1. Scientific notation: 1,000,000,000,000,000,000 = 1 x 1018
f. (e.g.) One sheet of paper is about 10,000 ATOMS in THICKNESS.
1. Scientific notation: 10,000 = 1 x 104
g. (e.g.) Avogadro’s number
1. Scientific notation: 602,000,000,000,000,000,000,000 = 6.02 x 1023
C. Steps for writing a NUMBER in standard numerical format from a SCIENTIFIC
NOTATION format:
1. REVERSE the process as indicated by the EXPONENT
a. When the EXPONENT is a positive number, move the DECIMAL point
in the single digit factor to the RIGHT the same number of place value
positions as indicated by the EXPONENT number which will make the
standard number a WHOLE number
1. (e.g.) 1 x 105 = 100,000
1.5 x 108 = 150,000,000
b. When the EXPONENT is a negative number, move the DECIMAL point
in the single digit factor to the LEFT the same number of place value
positions as indicated by the EXPONENT number which will make the
standard number a DECIMAL fraction
1. (e.g.) 4 x 10 -7 = 0.0000004
c. PRACTICE:
(1) 7 x 10 -3 = 0.007
(2) 4.13 x 10 -8 = 0.0000000413
(3) 5.02 x 10 6 = 5,020,000
(4) 2.9 x 10 -4 = 0.00029
(5) 8.61 x 10 -2 = 0.0861
(6) 4.971 x 10 5 = 497,100
(7) 8 x 10 3 = 8,000
(8) 3.382 x 10 -3 = 0.003382
(9) 9.009 x 10 -6 = 0.000009009
(10) 7.75128 x 10 7 = 77,512,800
6.34 x 10 -6 = 0.00000634