A baby marmot lies next to its mama on a sunlit log in the mountains. A researcher is studying how much solar energy the baby marmot absorbs over time. Due to the remote location, all quantities are approximated or measured with some instrument error.

The baby marmot's exposed surfaced error is estimated to be A=0.031 m2. At the altitude, the solar irradiance is measured at P=1.2×103 W/m2. The baby marmot lies still for t=25 minutes.

The energy absorbed by the baby marmot, in Joules, is given by E=P⋅A⋅t.

The total market value of all the gold in the world is 2.7×1013 US dollars.

Olympic swimming pools have dimensions 50m by 25m by 2m. It is given that 1cm3 of gold weighs 19g.

The largest number a computer memory chip can store is 2n, where n is the number of bits the computer chip has.

Perplex makes two chips, version 1 with 32 bits, and version 2 with 64 bits. The largest number that can be stored on version 2 is k times the largest number that can be stored on version 1.

A spherical raindrop has a diameter of 2mm.

In the following parts of the problem, give all your answers in the form a×10k where 1≤a<10 and k∈Z.

During a large thunderstorm, 7000m3 of water falls.

The number of HX2​O molecules in 1mL is 3.34×1022.

The area swept out by Earth's orbit each day is 1.92×1014km2. The height of the Empire State Building is 443m.

A single flake of fish food is a cube with volume 1.56×10−5 cm3. Martha's prize fish, Immanuel, eats an average of 6 flakes per minute. She typically gives him 20 flakes each day.

Immanuel's tank has a volume of 4.8×104 cm3.

A scientist is measuring how the concentration of a chemical in a lab reaction decreases over time. The exact concentration C(t), in mol/L, at any time t is given by the function

Due to technological limitations, the measured concentration, m, is known to the nearest 0.01mol/L.

Since the concentration changes with time, the percent error E%, also changes with time.

The exact diameter of the moon is 3480km. Arjun measures the diameter of the moon to be 3500km.

Using his measurement, Arjun estimates the surface area of the moon to be A=a×10kkm2, where 1≤a<10.

Arjun uses a millimeter ruler to measure the dimensions of a postage stamp.

The height h of the stamp satisfies the inequality 13≤h<14.

The pH of a liquid, a measure of its acidity, is given by pH=−log(H+)+23.78, where (H+) is the number of hydrogen ions in one liter of the liquid. Jack's stomach contains 300mL of digestive acid with a pH of 2.1.

Olympic swimming pools have dimensions 50m by 25m by 2m.

Lye, or NaOH, has a pH of 12.

Jack drinks a protein shake with volume V and pH 7. The time it takes to digest the shake is given by t=3+log(pH+1.4)⋅V, where pH is the pH of the food ingested.