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Implied accuracy in scientific notation

bergausstein

Active member
Jul 30, 2013
191
i just want to understand what i read in my algebra book. here what it says:

a measurement of 83200 ft. converted to (8.32)x10^4 ft. is now accurate to the nearest hundred feet. if we write (8.320)x10^4 the measurement is now accurate to the nearest ten feet.

i want to know why it is nearest to a hundred feet in the first conversion and nearest to ten feet in the second.

thanks!
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Re: need help in my algebra!

It may help to force the mantissa (the number which is multiplied by a power of ten) to be an integer:

\(\displaystyle 8.32\,\times\,10^4\text{ ft}=832\,\times\,10^2\text{ ft}\)

We see we have a multiple of 100 ft.

\(\displaystyle 8.320\,\times\,10^4\text{ ft}=8320\,\times\,10\text{ ft}\)

We see we have a multiple of 10 ft.
 

bergausstein

Active member
Jul 30, 2013
191
Re: need help in my algebra!

thanks!