How do you write 0.000000258 in scientific notation?

Our coefficient (#c#) needs to be between 1 and 10, but cannot be 10 (#1<=c>10#). To do this, let's move our decimal point 7 units to the right. Since we moved it to the right, we will have a negative exponent. This leaves us with our answer of #2.58*10^-7#.

Given:

#0.000000258#

I am using this approach to help you fix in your mind what is happening.

#color(brown)(0.000000258" is the same value as all the following:")#
#color(white)("d")#
#0.00000258 xx 1/10^1#
#color(white)("d")#
#0.0000258 xx 1/10^2#
#color(white)("d")#
#0.000258 xx 1/10^3#
#color(white)("d")#
#0.00258 xx 1/10^4#
#color(white)("d")#
#0.0258 xx 1/10^5#
#color(white)("d")#
#0.258 xx 1/10^6#
#color(white)("d")#
#color(brown)(2.58 xx 1/10^7)#

Another way of writing #2.58 xx 1/10^7" is "2.58xx10^(-7)#

#color(brown)(2.58xx10^(-7)larr" Scientific notation")#

People do not state it like this but it is actually what is happening.
The decimal point stays where it is. At each stage you move the digits to the left by 1 place.

counting in unit's #-> color(white)("ddddd") 5.0#

counting in ten's #-> color(white)("ddd.d")50.0#

counting in hundreds#-> color(white)("d")500.0#