Unit Consistency and Conversions

Problems for solution without assistance

Problem 1

How many nanoseconds does it take light to travel 1 m in a vacuum?

Problem 2

The density of water is 1.00 g/cm³. What is this value in kilograms per cubic meter?

Problem 3

Starting with the definition of 1 in = 2.54 cm, find the number of miles in 1 kilometer.

Problem 4

The volume of liquid in a can of soft drink is given as 0.355 liters. Using only the conversion of 1L =1000 cm³ and 1 in = 2.54 cm, express this volume in cubic inches.

Problem 5

While driving in a strange land you see a speed limit sign on the highway that reads 96,000 furlongs per fortnight. How many miles per hr is this? One furlong is 1/8 of a mile, and a fortnight is 14 days.

Problem 6

The gasoline consumption of a small car is advertised as 12.0 km/L How many miles per gallon is this?

Problem 7

Estimate the percent error in measuring a) a distance of about 65 cm with a meter stick,
b) a mass of about 16 g with a chemical balance;
c) a time interval of about 4 min with a stopwatch.

Problem 8

The mass of planet Saturn is 5.69 xl0²⁶ kg, and its radius is 6.03 xl0⁷ m.
a) Compute the average density of Saturn in kg/m³, using powers-of-ten notation and the correct number of significant figures,
b) Express the density of Saturn in g/cm3. An object will float in water if its average density is less than that of water, 1.00 g/cm3. Will an object with the same average density of Saturn float or sink in water?

Examples of solutions

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