Question

One inch is defined as 2.54 cm. How many feet are in 1559 cm? Express the answer in the proper number of significant figures.
A) 5 ´ 101 ft
B) 51 ft
C) 51.1 ft
D) 51.15 ft
E) 51.148 ft

Answer 1

c

Answer 2

The answer should be D using correct significant figures. Since your least precise place is the hundredths.

Answer 3

for addition and subtranction you use numbers after the decimal place, for multplication and division you use total sig figs. which is 3 in this case so your number should only contain 3 sig figs.

Answer 4

Ah, I understand since the least accurate is 2.54.

Answer 5

D. There are (presumably) 4 sig digs in your measured data, 1559cm. To convert to inches you divide by 2.54 (to get inches) and then by 12 (to get feet). However, both 2.54 and 12 are "exact numbers," meaning they have no measurement uncertainty -- they are NOT the result of measurements, but of definitions. (That is, there are 12 inches in a foot by definition, and 2.54 cm in an inch by definition.)

When you manipulate data by multiplying or dividing exact numbers, you do not change its precision. Since you started off with 4 sig dig precision in your data, you end up with 4 sig dig precision in your answer. Only answer D has 4 sig dig.

Answer 6

alright I would like you all to look at this http://www.cartage.org.lb/en/themes/sciences/chemistry/miscellenous/helpfile/units/Multiplication.htm but just incase i will also cut and paste as section out of it

if you multiply 1.23 and 4.567, you get an answer of 5.61741. 1.23 has three significant figures, 4.567 has four. Therefore, the answer should have three significant figures, since three is less than four. The properly rounded answer would be written as 5.62.


Now allow me to set up the question in a factor label problem,

\[1559 cm(\frac{1 inch}{2.54 cm})(\frac{1 foot}{12 inch})=51.14829\]

Now we look at our numbers with the least amount of sig figures which is 2.54 cm and the rest of the numbers are exact. Now we count back 3 sig figs from the answer and round the trailing, 51.1 and the next is 4 so we stay at 51.1 ft.

Answer 7

The problem with your analysis, zbay, is that 2.54 is just as much an exact number as is the 12 or two 1s in your equation. All of them are defined, and have zero measurement error. You should not be counting sig figs on any of them. The only sig figs that matter are in the original data, 1559cm.

Answer 8

http://www.dmacc.edu/instructors/rbwollaston/Significant_figures.htm

number 7.) 2.54 cm = 1 in (The 2.54 has 3 significant figures.