# Implied accuracy in scientific notation

#### bergausstein

##### Active member
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
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
Re: need help in my algebra!

thanks!