Question

How do you multiply expressions written in scientific notation?

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*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)`

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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`

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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`