# How is 0.00124 expressed in proper scientific notation?

##### 1 Answer

#### Explanation:

A number expressed in **scientific notation** must 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)#

For *normalized* scientific notation, the mantissa must satisfy the condition

#1 <= |m| < 10#

Your starting number can be written as

#color(blue)(0.00124) * 10^color(purple)(0)#

Your goal here will be to move the decimal place **to the right** until the mantissa satisfies the above condition. **For every position** that you move the decimal to the right you must **subtract**

So, start moving the decimal place to the right

#color(blue)(0.0124) * 10^color(purple)(-1) -># one position

#color(white)(0)color(blue)(0.124) * 10^color(purple)(-2) -># two positions

#color(white)(00)color(blue)(1.24) * 10^color(purple)(-3) -># three positions

At this point, the mantissa satisfies the required condition

#1 <= color(blue)(1.24) < 1#

which means that you have found the scientific notation for your original number

#0.00124 = 1.24 * 10^(-3)#