To put numbers into scientific notation:
- Place a decimal between the first 2 (non-zero) 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 non-zero 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 non-zero digits are 2 and 9, so we put a decimal between them and include any other non-zero 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 106
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