Question

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

Thanks!

Answer 1

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`.