Question

example problem 2.4 using conversion factors in ancient egypt, small distances were measured in egyptian cubits. an egyptian cubit was equal to 7 palms, and 1 palm was equal to 4 fingers. if 1 finger was equal to 18.75 mm, convert 6 egyptian cubits to meters. analyze the problem a length of 6 egyptian cubits needs to be converted to meters. known length = 6 egyptian cubits 7 palms = 1 cubit 1 palm = 4 fingers 1 finger = 18.75 mm 1 m = 1000 mm solve for the unknown use dimensional analysis to convert the units in the following order. cubits → palms → fingers → millimeters → meters 6 cubits × 7 palms / 1 cubit × 4 fingers / 1 palm × 18.75 mm / 1 finger × 1 meter / 1000 mm =? m 6 cubits × 7 palms / 1 cubit × 4 fingers / 1 palm × 18.75 mm / 1 finger × 1 meter / 1000 mm = 3.150 m evaluate the answer each conversion factor is a correct restatement of the original relationship, and all except for the desired unit, meters, cancel. ractice problems 1. the speedometer at right displays a cars speed in miles per hour. what is the cars speed in km/h? (1 km = 0.62 mile) 2. how many seconds are in 24 h? 3. challenge vinegar is 5% acetic - acid and has a density of 1.02 g/ml. what mass of acetic acid, in grams, is present in 100 ml of vinegar? section 2.2 assessment 24. main idea describe how scientific notation is used to express very large or very small numbers. 25. express the numbers 0.00087 and 5400000 in scientific notation. 26. write the measured distance quantities 3.2×10^(-2) km and 8.97×10^(4) cm in regular notation. 27. write a conversion factor relating cubic centimeters and milliliters. 28. solve how many millimeters are there in 2.5 km? 29. explain how dimensional analysis is used to convert units. 30. apply concepts a classmate converted 1200 cm to m and got 120000 m as the answer. explain why this answer is incorrect and identify the source of the error. 31. organize create a flowchart that shows how to convert between units of length in the metric system.

Explanation:

Step1: Identify the conversion - factor for miles to km

Given that $1\ km = 0.62\ mile$, then the conversion factor to convert miles to km is $\frac{1\ km}{0.62\ mile}$.

Step2: Assume the speed in miles per hour

Let the speed of the car in miles per hour be $v_{mi/h}$. To convert it to km/h, we multiply the speed in miles per hour by the conversion factor.
If $v_{mi/h}$ is the speed in miles per hour, then $v_{km/h}=v_{mi/h}\times\frac{1\ km}{0.62\ mile}$.

For example, if the speedometer shows $v_{mi/h} = 60\ mi/h$, then $v_{km/h}=60\times\frac{1}{0.62}\approx96.77\ km/h$.

Answer:

To convert the speed of the car from miles per hour to km/h, multiply the speed in miles per hour by $\frac{1}{0.62}$. The formula is $v_{km/h}=v_{mi/h}\times\frac{1\ km}{0.62\ mile}$.