MHB Implied accuracy in scientific notation

AI Thread Summary
The discussion clarifies how scientific notation indicates measurement accuracy. The conversion of 83200 ft to (8.32)x10^4 ft implies accuracy to the nearest hundred feet, as the mantissa is a multiple of 100. In contrast, (8.320)x10^4 ft suggests accuracy to the nearest ten feet, since the mantissa is a multiple of 10. This distinction arises from the number of significant figures in the mantissa, which directly affects the precision of the measurement. Understanding this relationship helps in interpreting scientific notation accurately.
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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!
 
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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:

$$8.32\,\times\,10^4\text{ ft}=832\,\times\,10^2\text{ ft}$$

We see we have a multiple of 100 ft.

$$8.320\,\times\,10^4\text{ ft}=8320\,\times\,10\text{ ft}$$

We see we have a multiple of 10 ft.
 
Re: need help in my algebra!

thanks!
 
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