Question

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

Answer 1

Answer:

See explanation

Step-by-step 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:

$10(5*10^{-1}+150*10^{-3}) = 5*10^{-1} \times 10+150*10^{-3} \times 10$

We can now use rules of exponents to simplify further:

$10(5*10^{-1}+150*10^{-3}) = 5*10^{-1} \times 10^{1} +150*10^{-3} \times 10^{1}$

$10(5*10^{-1}+150*10^{-3}) = 5*10^{-1 + 1} +150*10^{-3 + 1}$

$10(5*10^{-1}+150*10^{-3}) = 5*10^{0} +150*10^{-2}$

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

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

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