Dividing Scientific Notation Numbers
To divide numbers in scientific notation:
- Divide the base numbers
- Subtract the exponents of the tens
- Adjust the base number to have one digit before the decimal point by raising or lowering the resulting exponent of the ten
Here are the steps to divide two numbers in scientific notation:
To divide two numbers in scientific notation, divide their coefficients and subtract their exponents. In either case, the answer must be converted to scientific notation.
- Divide the coefficients–round to the number of significant figures in the coefficient with the smallest number of significant figures.
- Subtract the exponents.
- Convert the result to scientific notation.
For example, divide 1.6×107 by 2×10-2:
First, the base numbers are 1.6 ÷ 2 = 0.8
Then, subtracting the exponents makes 7 – (-2) = 9
Finally, 0.8×109 is not valid scientific notation because we can only have 1 non-zero digit left of the decimal. Moving the decimal 1 place to the right means decreasing the exponent by 1. Our final answer is 8×108
Distribute the division across both the coefficients and the powers of ten. Next, divide the two coefficients: 3.5/5 = (35/10)/5 = (35/5)/10 = 7/10 = 0.7. Then, divide the two powers of ten by subtracting their exponents: since -6 – (-2) = -6 + 2 = -4, then 10-6 / 10-2 = 10-4. Finally, combine your two answers and convert to scientific notation. In symbols:
(3.5 × 10-6) / (5 × 10-2)
= (3.5 / 5) × (10-6 / 10-2)
= (0.7) × (10-4)
= 7 × 10-5