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