Question

dimensional analysis quiz
the following questions will assess your knowledge of dimensional analysis. use the
conversion factors in the table below to help with your calculations.
multiple choice (1 pt each = 5 pts)

1. which of the following is the best definition of dimensional analysis?

a) rounding numbers to the nearest whole number
b) using units to guide the setup of conversions between different measurements
c) measuring objects using rulers or graduated cylinders
d) adding and subtracting numbers with labels

1. which conversion factor is equal to 1?

a) \\( \frac { 1 f t } { 24 i n } \\)
b) \\( \frac { 1000 m } { 1 k m } \\)
c) \\( \frac { 1 h r } { 100 s e c } \\)
d) \\( \frac { 10 g } { 1 m g } \\)

1. how many centimeters are in 2.3 meters?

a) 23
b) 230
c) 2300
d) 0.023

1. which of the following shows correct unit cancellation?

a) \\( 5 mathrm { km } \times \frac { 1 mathrm { m } } { 1000 mathrm { m } } \\)
b) \\( 10 mathrm { g } \times \frac { 1000 mathrm { g } } { 1 mathrm { mg } } \\)
c) \\( 60 mathrm { min } \times \frac { 1 mathrm { hr } } { 60 mathrm { min } } \\)
d) \\( 4 mathrm { ft } \times \frac { 1 mathrm { ft } } { 12 mathrm { in } } \\)

1. a student drives 45 miles in 1 hour. what is this speed in ft/s?

a) 22 ft/s
b) 44 ft/s
c) 66 ft/s
d) 88 ft/s

Explanation:

Question 1

Dimensional analysis uses units to set up conversions between different measurements. Option a is rounding, c is measuring, d is arithmetic with labels. So b is correct.

A conversion factor equal to 1 has equivalent quantities in numerator and denominator. 1 km = 1000 m, so $\frac{1000\ m}{1\ km}$ is 1 (since 1000 m = 1 km). Option a: 1 ft ≠ 24 in; c: 1 hr ≠ 100 sec; d: 10 g ≠ 1 mg.

Step1: Recall the conversion factor (1 m = 100 cm)

To convert meters to centimeters, multiply by 100. So, $2.3\ m\times\frac{100\ cm}{1\ m}$

Step2: Perform the calculation

$2.3\times100 = 230$

Answer:

b) Using units to guide the setup of conversions between different measurements

Question 2