Question

5) How many significant figures are in the number `2.34xx10^12`?

Answer 1

`3`

Explanation:

The thing to remember about numbers expressed in scientific notation is that you can determine how many significant figures they have by examining the mantissa.

For a number written using normalized scientific notation, you have

`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)`

For normalized scientific notation, you must have

`1 <= |m| < 10`

Now, the number of sig figs for a number expressed in scientific notation is always given by the number of sig figs in the mantissa.

In this case, the mantissa is

`m = 2.34`

As you know from the rules we have for determining how many sig figs we have in a number, any non-zero digit is significant. In this case, the mantissa contains three non-zero digits, `2`, `2`, and `4`, which means that it has three sig figs.

Therefore, the number

`2.34 * 10^12 ->` three sig figs

will also have three sig figs, all present in the mantissa.