How many feet are in  43.0 miles? how to round to correct significant figures

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hwbruce's profile pic

hwbruce | High School Teacher | (Level 1) Adjunct Educator

Posted on

You should use dimensional analysis for a problem like this.  Your asking for the number of feet in 43.0 miles.  I would set up my problem like this:

? ft = 43.0 miles

You need to think of the conversion factors needed to change your units.  For this problem, you only need to know that 1 mile = 5280 ft.  Plug it into your problem like this:

? ft  = 43.0 miles x 5280 ft

                             1 mile

Mathematically you should get the answer 227,040 ft.  Now we need to focus on sigfigs.  The rules for sigfigs depend upon the math you are doing.  Since we did multiplication/division, the rule states that you round to the least number of sigfigs used.  For dimensional analysis, conversion factors are assumed to have infinite precision.  We say that 1 ft = 12 inches, but we could truly say that 1.00000 (infinite zeroes) = 12.00000 (infinite zeroes) inches.  It's a defined conversion, not something measured.  In other words, your starting number, 43.0, is your focus.  It has 3 sigfigs (zeroes after the decimal are significant), so your answer can only have 3 sigfigs.

227, 040 ft --> 227,000 ft

teachelderj's profile pic

teachelderj | Elementary School Teacher | (Level 1) Adjunct Educator

Posted on

Start with what is known. 1 mile equals 5280 feet. To determine the total number of feet in 43 miles. 

Here's the conversion factor:  1 mile=5280 feet 

Take 43 miles X  5280 feet/1 mile. The mile units will cancel each other out and you will mulitiply 43X5280 feet

your answer will be: 227, 040 feet

Know to round to significant figures. Seek to write the figure  with one decimal place and use exponents. Therefore , count the number of places starting from zero to the left and stop counting once you reach the second #2. As a result, the number written in scientific notation is 2.27 X 10^5

mountaingirl's profile pic

mountaingirl | High School Teacher | eNotes Newbie

Posted on

When do a conversion like this one you need to look at where you are where you are going.  The example starts with miles and needs to be converted to feet.  

miles ----> feet

You must determine if there is a direct conversion factor between miles and feet.

1 mile = 5,280 feet

(43 miles) X (5280 ft/1 mile) = 227,040 ft

To put this answer into the correct significant figures you must look at the value you began with and determine the number of significant figures it has. 

43 miles = 2 significant figures

Note: you are not considering the 5280 ft because it is a conversion factor. Significant figures show accuracy of measurement therefore it only applies to the original measurement of 43 miles.

Therefore, based on 2 significant figures the answer would be 2.2 * 10^5 ft.

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jeffmoriarty's profile pic

jeffmoriarty | (Level 1) eNoter

Posted on

1 mile has 1.60934 km

1 km has 1000 m

1 m has 3.281 feet

So 43 miles would be equivalent to 43 miles x 1.60934 km/miles x 1000 m/km x 3.281 feet/m 

 = 227050.515 foot

Hope this helped

penu's profile pic

penu | eNotes Newbie

Posted on

1 mile has 5280 feet,

so 43 miles will have 43 x 5280 = 227,040 feet.

Kindly note that because of significant figures answers may vary slightly (you can compare this answer with that of educator 1).

sezra's profile pic

sezra | (Level 1) eNoter

Posted on

1 mile has 5,280 feet.

5,280 feet x 43.0 miles = 227,040 feet

Basically, if you can get rid of zeroes in scientific notation, then they are not significant, so the inclusion of the tenths in "43.0" isn't significant, and isn't necessary for your answer to include.

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