Question

AcellusPerform the followingoperation and express theanswer in scientific notation.2.60x10-5 x 2.10x10-5[? ]x101)Coefficient (green)Exponent (yellow)Enter

Answer 1

Step 1 - Understanding how to work with scientific notation

Scientific notation is used as an easier means of expressing too large or too small numbers. Incredible as it may seen, it simplifies math expressions, not overcomplicated them. That's because we can use a little trick when dealing with scientific notation: we multiply the numbers and deal with the scientific notation next.

There are some rules we need to know about scientific notation concerning powers:

a)

`10^x*10^y=10^(x+y)`

This is the most important one. There are others, of course:

b)

`(10^x)/(10^y)=10^(x-y)`

These two rules will be very useful when dealing with scientific notation.

Also remember that in scientific notation the number must be between 1 and 10. We could never write, for example:

`25*10^4`

We would have to express it as:

`2.5*10^5`

Step 2 - Using scientific notation rules to solve the exercise

The expression we want to solve is:

`2.60*10^(-5)*2.10*10^(-5)`

Let's deal with the numbers first:

`2.60*2.10=5.46`

Now the powers (note that we can apply the rule we saw in step 1, a):

`10^(-5)*10^(-5)=10^(-5+(-5))=10^(-10)`

Finally, let's put it all together:

`5.46*10^(-10)`

Always remember to check if the number is between 1 and 10. In this case, it is, so we are done. The answer is thus 5.46*10^(-10).

Coefficient: 5.46

Exponent: -10