Question

Explain how the exponent of 10 changes when you multiply a number written in scientific notation by 100. Show an example.

Answer 1

Expressions can be easily multiplied when written in scientific notation by:
1. First, multiplying the numbers other than the powers of 10.
2. Second, multiplying the powers of 10
And then, writing them as a product.

Let us take the general case first.

Multiplying two numbers x⋅10m and y⋅10n

First, multiplying the numbers other than the powers of 10, we get:
x⋅y=xy

Second, multiplying the powers of 10 we get
10m⋅10n=10m+n

And then writing them as a product, we get
xy⋅10m+n

Therefore, (x⋅10m)⋅(y⋅10n)=xy⋅10m+n

Note: When the bases of 2 numbers are equal, their powers can be added up!
Examples: 
1). 2a⋅2b=2a+b
2) 33⋅37=33+7=310

Now, let's take some specific examples.

Q: Multiply 1.2⋅103 and 2.3⋅104

A:

(1.2⋅103)⋅(2.3⋅104)
=(1.2⋅2.3)⋅(103+4)
=2.76⋅107

Q: Multiply 9.32⋅1021 and 8.21⋅1032

A:

(9.32⋅1021)⋅(8.21⋅1032)
=(9.32⋅8.21)⋅(1021+32)
=76.5172⋅1053

Notice that this answer is not in the standard form. So, converting this into standard form, we get:

=7.65172⋅1054


Hope this helps
Have a good day!