# Question #e817a

##### 1 Answer

#### Explanation:

As you know, a number written in **scientific notation** will have the form

#color(white)(aa)color(blue)(m) xx 10^(color(purple)(n) color(white)(a)stackrel(color(white)(aaaaaa))(larr))color(white)(acolor(black)("the")acolor(purple)("exponent")aa)#

#color(white)(a/acolor(black)(uarr)aaaa)#

#color(white)(color(black)("the")acolor(blue)("mantissa")a)#

In the vast majority of cases, you will be dealing with *normalized scientific notation*, which must have

#1 <= |m| < 10" " " "color(orange)("(*)")#

Now, the thing to remember about scientific notation and significant figures is that the *mantissa* must * always* have the

**same number of sig figs**as the number written in standard notation.

In your case, the number **five sig figs**, which means that the mantissa must also have five sig figs.

All you have to do now is convert **and** has five sig figs.

As you know, zeros that *follow* a decimal point are significant **if** they also follow a non-zero digit. In this case, you can write

#2.0000 -># onenon-zero digit andfoursignificant zeros for a total offive sig figs

This means that the scientific notation for

#2000.0 = 2.0000 * 10^(3)#

The exponent is *positive* because you're moving the decimal point **to the left**.