Scientific Notation Division

Scientific Notation Division

When dividing numbers in scientific notation, use two separate parts: the numbers in front and the powers of 10.

1) Divide the coefficients

Divide the decimal numbers first. For example, if the problem looks like \((a \times 10^m) \div (b \times 10^n)\), start with \(a \div b\).

2) Subtract the exponents

For powers of 10, divide by subtracting exponents: \[ 10^m \div 10^n = 10^{m-n} \] So the result becomes the coefficient quotient times a power of 10.

3) Put the answer in scientific notation

Make sure the coefficient is at least 1 and less than 10. If it is not, move the decimal point and adjust the exponent accordingly.

4) Check your work

Estimate the size of the result. If the original number was larger than the divisor, the answer should make sense as a larger or smaller value based on the exponent difference. You can also multiply your final answer by the divisor to see if you get back the original number.

Quick example

If \(6 \times 10^4 \div 2 \times 10^2\), divide 6 by 2 to get 3, and subtract exponents to get \(10^{4-2} = 10^2\). The final answer is \(3 \times 10^2\).