Let's estimate the answers to these problems by rounding each number to 1 significant figure and then calculating.

a) $\frac{3.8 \times 9.1}{0.51}$

1. Round each number to 1 significant figure:

   • $3.8 \approx 4$
   • $9.1 \approx 9$
   • $0.51 \approx 0.5$

2. Now substitute the rounded numbers: $\frac{4 \times 9}{0.5} = \frac{36}{0.5}$

3. Calculate the estimate: $\frac{36}{0.5} = 36 \times 2 = 72$

Answer to a) = 72

b) $\frac{29.4 \times 39.9}{0.17}$

1. Round each number to 1 significant figure:

   • $29.4 \approx 30$
   • $39.9 \approx 40$
   • $0.17 \approx 0.2$

2. Now substitute the rounded numbers: $\frac{30 \times 40}{0.2} = \frac{1200}{0.2}$

3. Calculate the estimate: $\frac{1200}{0.2} = 1200 \times 5 = 6000$

Answer to b) = 6000

Let me know if you'd like more details on this method or need further explanations!

Here are 5 related questions:

1. What does it mean to round to one significant figure?
2. How do you perform multiplication and division with numbers in scientific notation?
3. Why is estimation useful in everyday calculations?
4. How does rounding affect the precision of your answers?
5. Can you use a similar estimation method for addition and subtraction?

Tip:

When estimating answers, rounding to 1 significant figure is a quick way to approximate without doing complex calculations, but it sacrifices accuracy for speed.