Let's solve these two problems step by step by rounding each number to 1 significant figure.

(a) $\frac{8.2 \times 6.7}{0.46}$

1. Rounding to 1 significant figure:

   • 8.2 rounds to 8.
   • 6.7 rounds to 7.
   • 0.46 rounds to 0.5.

2. Estimate the calculation: $\frac{8 \times 7}{0.5} = \frac{56}{0.5} = 112.$

So, the estimated answer for (a) is 112.

(b) $\frac{23.4 \times 13.9}{0.18}$

1. Rounding to 1 significant figure:

   • 23.4 rounds to 20.
   • 13.9 rounds to 10.
   • 0.18 rounds to 0.2.

2. Estimate the calculation: $\frac{20 \times 10}{0.2} = \frac{200}{0.2} = 1000.$

So, the estimated answer for (b) is 1000.

Let me know if you'd like further details on these calculations!

Here are five relative questions to expand your understanding:

1. How do you round a number to 1 significant figure?
2. Why is it useful to estimate answers by rounding?
3. What would the exact answers be without rounding?
4. Can rounding affect the accuracy of an estimate in some cases?
5. What other methods can be used to estimate calculations quickly?

Tip: When rounding for estimates, try to balance simplicity with accuracy—don't overestimate or underestimate the result too much.