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Chapter 2: Measurement and Problem Solving Convert between units. Convert units raised to a power. How many seconds are in 532 days? Units are multiplied, divided, and canceled like any other algebraic quantities. Using units as a guide to solving problems is called dimensional analysis. Always write every number with its associated unit. Do not let units appear or disappear in calculations. Units must flow logically from beginning to end. Conversion factors are ratios constructed from any two quantities known to be equivalent. Conversion factors can be inverted because they are equal to 1 and the inverse of 1 is 1. In solving problems, always check if the final units are correct, and consider whether or not the magnitude of the answer makes sense. When converting quantities with units raised to a power, the conversion factor must also be raised to that power. Convert 7.8 km to miles. Convert 0.825 m to millimeters. One lap of a running track measures 255 m. To run 10.0 km, how many laps should you run? A circle has an area of 2659 cm2. What is its area in square meters? An automobile engine has a displacement (a measure of the size of the engine) of 289.7 in.3 What is its displacement in cubic centimeters?