Hi Mackenzie,
To put numbers into scientific notation:
 Place a decimal between the first 2 (nonzero) digits
 Count the number of place values you have to shift to get from this new number to the original decimal number
 Copy the digits and write the “shifting” with a base “10” in exponential form
 If “shifting” to the RIGHT > the exponent will be positive
 If “shifting” to the LEFT > the exponent will be negative
For example, change the following into scientific notation:
a) 0.000 049
 The first 2 nonzero digits are 4 and 9, so we put a decimal between them: 4.9
 To move from the new decimal to the old decimal, we had to move it 5 places to the left, so the digit 5 is in our exponent with a base of 10. Since to get to the original decimal we must move to the left, our exponent is negative and our answer is then: 0.000 049 = 4.9 x 10^{5}
b) 2 930 000
 The first 2 nonzero digits are 2 and 9, so we put a decimal between them and include any other nonzero digits (after the decimal) if there are any: 2.93
 To move from the new decimal to the old decimal, we had to move it 6 places to the left, so the digit 6 is in our exponent with a base of 10. Since to get to the original decimal we must move to the right, our exponent is positive and our answer is then:2 930 000 = 2.93 x 10^{6}
Sara
Hi Mackenzie,
Let me look at a different example.
Write 0.0000178 in scientific notation.
I know that for scientific notation I am to have exactly one digit to the left of the decimal so I know the answer is
0.000 017 8 = 1.78 10^{??}
for some positive or negative inyeger ??. Look at 0.000 017 8 and 1.78. The decimal has moved 5 places so
0.000 017 8 = 1.78 10^{?5}
but is ? a plus or minus sign? If it were posivive I would have
1.78 10^{+5 }= 1.78 100 000 = 178 000
which is clearly wrong so it must be that
0.000 017 8 = 1.7 10^{5}
Penny
