You have three coins that are identical in appearance. One is counterfeit, and its mass is different from the mass of the two legitimate coins. You also have an equal-arm balance (a device that compares the masses of two objects and “balances” if they are equal). Describe how you can determine which is the counterfeit coin and whether it is heavier or lighter than the legitimate coins by making only two measurements with the balance.

Suppose that, in a laboratory exercise, you add 0.335 g of liquid to a 145.67-g ceramic bowl. After you heat the liquid for 25.01 s, you measure the mass of the bowl and liquid together to be 145.82 g. What was the average mass of liquid that evaporated each second?

You work in a hospital and are preparing a saline solution for a patient. This solution must have a concentration of 0.15 mol of NaCl (mass of one mole, 58.44 gram) per liter of solution. You have lots of volume-measuring devices, but the only mass-measuring tool you have is a balance that measures mass to the nearest 0.1 g. What is the minimum amount of solution you should mix?

A certain brand of soft drink contains 34 mg of caffeine per 355-mL serving. If one mole of caffeine has a mass of 194.19 g and you drink an average of two servings of this drink a day, how many caffeine molecules do you ingest in one year?

The odometer on your car says 23,456 km. To the correct number of significant digits, what should the odometer read after you drive 725 m a day for the next 20 days?

You are recording your car’s gas mileage. Your odometer measures to the tenth of a mile. The gas station pump displays gallons of gasoline dispensed to the thousandth of a gallon. Given these levels of precision, is there any difference in the precision of your calculation when you drive 40.0 miles or 400.0 miles?