Question

use significant figures to solve the following division problem. (6.6666 x 10^6 ks^3)/(2.0000 x 10^4 ks) = how many significant figures in the final answer? 3 4 5 6

Explanation:

Step1: Divide the coefficients

When dividing numbers in scientific - notation, divide the coefficients and subtract the exponents of 10. The coefficient of the first number is 6.6666 and the second is 2.0000. So, $\frac{6.6666}{2.0000}=3.3333$.

Step2: Subtract the exponents of 10

The exponents are 6 and 4. Using the rule $\frac{10^{m}}{10^{n}} = 10^{m - n}$, we have $10^{6-4}=10^{2}$.

Step3: Combine the results

The result of the division is $3.3333\times10^{2}$.

Step4: Determine significant figures

In multiplication and division, the result should have the same number of significant figures as the number with the fewest significant figures in the values being multiplied or divided. The number 2.0000 has 5 significant figures, and 6.6666 has 5 significant figures. So the result $3.3333\times10^{2}$ should have 5 significant figures.

Answer:

5