Question

How is the Distributive Property used to simplify operations with scientific notation

Answer 1

See explanation

Explanation:

Let a,b, and c be real numbers.

The distributive property says that:

`a(b + c) = ab + ac`

Assuming we want to simplify:

`10(5*10^(-1)+150*10^(-3))`

We apply the distributive property to get:

`10(5*10^(-1)+150*10^(-3)) = 5*10^(-1) * 10+150*10^(-3) * 10`

We can now use rules of exponents to simplify further:

`10(5*10^(-1)+150*10^(-3)) = 5*10^(-1) * 10^(1) +150*10^(-3) * 10^(1)`

`10(5*10^(-1)+150*10^(-3)) = 5*10^(-1 + 1) +150*10^(-3 + 1)`

`10(5*10^(-1)+150*10^(-3)) = 5*10^(0) +150*10^(-2)`

`10(5*10^(-1)+150*10^(-3)) = 5*1+1.50*10^(-2)x {10}^(2)`

`10(5*10^(-1)+150*10^(-3)) = 5*1+1.50*10^(-2 + 2)`

`10(5*10^(-1)+150*10^(-3)) = 5+1.50*10^(0) = 6.5 * {10}^(0)`