How many significant figures are in #92 * 10^3#?

Thanks!

1 Answer
Dec 4, 2016

Answer:

Two sig figs.

Explanation:

For starters, it's worth mentioning that the number given to you is not written in normalized scientific notation because the mantissa is #>= 10#.

Numbers expressed in normalized scientific notation take the general form

#color(white)(aa)color(blue)(m) xx 10^(color(red)(n) color(white)(a)stackrel(color(white)(aaaaaa))(larr))color(white)(acolor(black)("the")acolor(red)("exponent")aa)#
#color(white)(a/acolor(black)(uarr)aaaa)#
#color(white)(color(black)("the")acolor(blue)("mantissa")a)#

Here you need to have

#1 <= color(blue)(m) < 10#

In your case, the correct scientific notation for that number would be

#9.2 * 10^4#

The exponent increased by #1# unit because the mantissa decreased by an order of #10#.

Now, for numbers expressed in scientific notation, the number of significant figures is always given by the number of significant figures in the mantissa.

In this case, you have

#9.2 -># two non-zero digits #=# two sig figs

Therefore, the number

#9.2 * 10^4#

has two sig figs, #9# and #2#. The same can be said for

#92 * 10^3#

which also has two sig figs, #9# and #2#.