How to compute $\frac{63.5\times 0.5\times 10\times 60}{2\times 96500}$ without a calculator? Thankfully, I have been provided 4 options:
(a) $0.0987$
(b) $0.0897$
(c) $0.0798$
(d) $0.0789$

My attempt
$$\begin{aligned} \frac{63.5\times 0.5\times 10\times 60}{2\times 96500} &= \frac{63.5\times 0.5\times 600}{2\times 96500} \\ &= \frac{63.5 \times 300}{2\times 96500} \\ &= \frac{63.5\times 150}{96500} \\ &= \frac{635\times 15}{96500} \\ &= \frac{6350+3000+150+25}{96500} \\ &= \frac{9500+25}{96500} \\ &= \frac{9525}{96500} \end{aligned}$$
I'm still stuck with a long division.
$$\require{enclose} \begin{array}{rll}     0.09 && \\[-3pt]    96500 \enclose{longdiv}{9525}\kern-.2ex \\[-3pt]       \underline{868500} \\[-3pt]         \end{array}$$
[I couldn't display the long division nicely.]
We do not need to continue the long division further. We can understand the answer will be (a) by checking the options.

My question
This is actually a chemistry question from a competitive exam, which involves stoichiometric calculations. I had the most trouble doing the long division. I had to guess that the number is $9$ and had to multiply $9$ by $96500$. Is there a quicker and easier way?

Cancel $100$ from the denominator, and hand multiply the rest.
$$\frac{635\times3}{2\times965}=\frac{1905}{1930}\approx1$$
Therefore the answer is (a).
