Final answer:
In dividing numbers in scientific notation, divide the coefficients and subtract the exponents of the powers of ten. Ensure the resulting number respects the significant figures from the original numbers. Simplify the result, if necessary, to maintain appropriate notation.
Step-by-step explanation:
When tackling division involving numbers in scientific notation, the process involves subtracting exponents and dividing the coefficient (the number in front). If we are given an equation like 2.4 × 10¹³ divided by 8 × 10⁷, first, divide the coefficients (2.4 divided by 8) and subtract the exponents. The division of coefficients yields 0.3, and subtracting the exponents (13 - 7) gives us 6. Thus, the result will be 0.3 × 10⁶, which can be further simplified if necessary.
Applying similar logic, let's solve another division: If you have (8.552 × 10⁶) divided by (3.129 × 10³), you'd divide 8.552 by 3.129 to get approximately 2.733 and subtract the exponents to get 3 (since 6 - 3 equals 3). So, the result is 2.733 × 10³.
In situations requiring attention to significant figures, it's essential to round your final answer to reflect the least precision out of the numbers used in the calculation. For example, if you calculate 56.7 × 66.99 and get a long decimal, but 56.7 has only three significant figures, you would round your result to three significant figures as well.