We are given the problem of finding the upper and lower bounds of $1300 \div 45$, where both numbers are correct to 2 significant figures. The final answer must be correct to 2 significant figures.

1. Problem Description

We are given the problem of finding the upper and lower bounds of $1300 \div 45$, where both numbers are correct to 2 significant figures. The final answer must be correct to 2 significant figures.

2. Solution Steps

First, we determine the upper and lower bounds of each number.

Since 1300 is given to 2 significant figures, it is in the hundreds. Thus, the accuracy is to the nearest

1

0. So, $1300 = 1.3 \times 10^3$. The uncertainty is $\frac{1}{2} \times 10 = 5$.

Therefore, the upper bound of 1300 is $1300 + 50 = 1350$, and the lower bound is $1300 - 50 = 1250$.

Since 45 is given to 2 significant figures, it is in the tens. Thus, the accuracy is to the nearest

1. So the uncertainty is $\frac{1}{2} \times 1 = 0.5$.

Therefore, the upper bound of 45 is $45 + 0.5 = 45.5$, and the lower bound is $45 - 0.5 = 44.5$.

To find the upper bound of the division, we divide the upper bound of the numerator by the lower bound of the denominator:

Upper bound $= \frac{1350}{44.5} \approx 30.33707865 \approx 30.3$.

To find the lower bound of the division, we divide the lower bound of the numerator by the upper bound of the denominator:

Lower bound $= \frac{1250}{45.5} \approx 27.47252747 \approx 27.5$.

We are asked to correct the bounds to 2 significant figures.

Upper bound to 2 sf: 30

Lower bound to 2 sf: 27

However, the question asks for the answer "correct to 2 significant figures".

We recalculate the upper and lower bounds with more precision, as rounding intermediate values could introduce larger errors.

Upper bound $= \frac{1350}{44.5} \approx 30.33707865168539 \approx 30$

Lower bound $= \frac{1250}{45.5} \approx 27.47252747252747 \approx 27$

3. Final Answer

Upper bound: 30

Lower bound: 27