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

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Thanks!

Thanks!

##### 1 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

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**,

#92 * 10^3#

which also has **two sig figs**,