Question

Dimensional Analysis Method (also called conversion factor or unit analysis) (Appendix D: Dimensional Analysis, Page 397) o The dimensional analysis method uses equivalences written in _____________________ form. o Because the numerator and denominator of the fraction are equivalent, the value of the fraction is __________ o Multiplying by 1 does not change the quantity, but using an equivalence will change the units (or label) o In order for units to cancel they must be in _____________________________ of the fraction.

Answer 1

Dimensional analysis uses conversion factors written as fractions with a value of one, ensuring that multiplying by the factor changes the units but not the amount. It requires units to be on opposite sides of the fraction for them to cancel out.

Step-by-step explanation:

The dimensional analysis method uses equivalences written in fraction form. Because the numerator and denominator of the fraction are equivalent, the value of the fraction is one. Multiplying by 1 does not change the quantity, but using an equivalence will change the units (or label). In order for units to cancel they must be in opposite sides of the fraction.

Dimensional analysis, also known as the factor-label method, is a mathematical tool often used in physics and chemistry. It involves conversion factors to convert from one unit of measurement to another. This is very valuable because some measurements are easier to obtain or more accurate than others.

A conversion factor is essentially a ratio of two equivalent quantities expressed in different units, such as the equivalence of 2.54 cm to 1 inch. By using conversion factors in calculations, we can ensure that the final answer has the proper units, effectively cancelling units we don't want and producing the ones we do.

Answer 2

The dimensional analysis method uses equivalences written in fractional form. Because the numerator and denominator of the fraction are equivalent, the value of the fraction is 1. Multiplying by 1 does not change the quantity, but using an equivalence will change the units (or label). In order for units to cancel they must be in the numerator and the denominator of the fraction

Step-by-step explanation:

Dimensional analysis is a method of problem solving that takes into consideration the identity property of multiplication whereby the product of a number and 1 will always give the same number, that is 1 × n = n whereby the value "n" remains the same after the multiplication

Therefore, a fraction of two equivalent measurements but different units has a value of 1, and multiplying the equivalent fraction with another measurement with the same unit as the denominator of the fraction with a value of 1 changes the unit to that of the unit of the numerator