How do you multiply expressions written in scientific notation?

1 Answer
Nov 29, 2014

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*10^m and y*10^n

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

Second, multiplying the powers of 10 we get
10^m*10^n=10^(m+n)

And then writing them as a product, we get
xy*10^(m+n)

Therefore, (x*10^m)*(y*10^n)=xy*10^(m+n)


Note: When the bases of 2 numbers are equal, their powers can be added up!
Examples:
1). 2^a*2^b=2^(a+b)
2) 3^3*3^7=3^(3+7)=3^10


Now, let's take some specific examples.

Q: Multiply 1.2*10^3 and 2.3*10^4

A:

(1.2*10^3)*(2.3*10^4)
=(1.2*2.3)*(10^(3+4))
=2.76*10^7

Q: Multiply 9.32*10^21 and 8.21*10^32

A:

(9.32*10^21)*(8.21*10^32)
=(9.32*8.21)*(10^(21+32))
=76.5172*10^53

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

=7.65172*10^54