The significant figures are 7, 8, 9, and the trailing zero counts.

The trailing zero after the decimal point counts as a significant figure.

All non-zero digits are significant, so 1002 has 4 significant figures.

5000 has 1 significant figure unless specified otherwise (e.g., 5000. has 4 significant figures).

5000 has 1 significant figure unless specified with a decimal point (e.g., 5000. has 4).

Q = m * L = 1000 g * 2260 J/g = 2260000 J.

To round 0.0001234 to two significant figures, we look at the first two non-zero digits (1 and 2) and round up, resulting in 0.00013.

To round 0.05060 to three significant figures, we keep the first three significant digits (5, 0, and 6), resulting in 0.0506.

Q = m*c*ΔT = 1000 g * 4.2 J/g°C * (100°C - 20°C) = 4200 J.

At STP (Standard Temperature and Pressure), 1 mole of an ideal gas occupies 22.4 L at a pressure of 1 atm.

According to Avogadro's Law, 2 moles of gas will occupy double the volume, which is 44.8 L at STP.

The final temperature will be 50°C due to equal masses and specific heat capacities.

Using the principle of conservation of energy, the final temperature will be 50°C.

Using the principle of conservation of energy, the final temperature can be calculated to be 40°C.

According to the First Law of Thermodynamics, ΔU = Q - W. Here, ΔU = 100 J - 40 J = 60 J.

100 = 10^2, so 2x = 2, hence x = 1.

Since 0.01 = 10^(-2), we have x = -2.

Using the Ideal Gas Law, P = nRT/V = (2 moles * 0.0821 L·atm/(K·mol) * 300 K) / 10 L = 4.926 atm.

Heat lost by water = Heat gained by ice. 100g * 80°C = 200g * 334 J/g + 200g * (Tf - 0°C). Solving gives Tf = 20°C.

16 = 2^4 => x + 1 = 4 => x = 3

Using m1*T1 + m2*T2 = (m1 + m2)*Tf, we find Tf = (300*25 + 200*75) / (300 + 200) = 50°C.

Since 81 = 3^4, we have 3^(2x) = 3^4, thus 2x = 4, giving x = 2.

Since 64 = 4^3, we have x = 3.

According to the first law of thermodynamics, ΔU = Q - W. Here, ΔU = 500 J - 200 J = 300 J.

125 = 5^3, so x + 1 = 3, hence x = 2.

Since 25 = 5^2, we have 5^(x-1) = 5^2, thus x - 1 = 2, giving x = 3.

125 = 5^3 => x = 3

Since 25 = 5^2, we have 5^x = 5^2, thus x = 2.

49 = 7^2, so x = 2.

64 = 8^2, so x = 2.