Question $4$

$1$ pts

Suppose you break down a problem into steps with intermediate numbers. You must hold on to more digits in these steps than the final answer's significant digit so that you do not lose precision.

For example, calculate the answer to $504\mathrm{.}4272\mathrm{.}18+439\mathrm{.}3536\mathrm{.}45$ and round to the nearest one$-$hundredth. The correct answer is $52,423\mathrm{.}34.$ If the problem were broken down into steps, then these are the products: $504\mathrm{.}4272\mathrm{.}18=36,409\mathrm{.}0356$ and $439\mathrm{.}3536\mathrm{.}45=16,014\mathrm{.}3075.$ The precise answer is the sum: $36,409\mathrm{.}0356+16,014\mathrm{.}3075=52,423\mathrm{.}3431.$ After rounding, the final answer is $52,423\mathrm{.}34.$

If we incorrectly rounded the products to only the hundredth, then we would have gotten $36,409\mathrm{.}04+16,014\mathrm{.}31=52,423\mathrm{.}35,$ which is $0\mathrm{.}01$ off from the correct answer.

Therefore, hold onto at least $2-4$ digits past the final answer's significant digit until you get to the very end of the problem. Then, you can round.

Question: What is the answer to this equation, rounded to the nearest hundredth: $\frac{67}{0\mathrm{.}05}(1-\frac{1}{{1\mathrm{.}05}^{30}})=?[$Be careful to follow the correct order of operations.$]$

$1,029\mathrm{.}81$

$1,031\mathrm{.}80$

$1,029\mathrm{.}92$

$1,029\mathrm{.}95$

$1,031\mathrm{.}72$