simplify: q in bio

Question

(600 x 10^6)(0.0007 x 10^8) over (700,000 x 10^-12)(0.00003)

Answer 1

Let's start by converting everything into the proper scientific notation. Remember, moving decimals to the left adds to the exponent and moving to the right subtracts the exponent:

600 * 10⁶ → 6.0 * 10⁸

.0007 * 10⁸ → 7.0 * 10⁴

700,000 * 10^-12 → 7.0 * 10^-7

0.00003 → 3.0 * 10^-5

 

That gives us the following:

(6 * 10⁸ * 7 * 10⁴) / (7 * 10^-7 * 3 * 10^-5)

 

We have a 7 in the numerator and denominator, so those cancel out. We also have a 6 in the numerator and 3 in the denominator, so we can factor out a 3, giving us a 2 in the numerator and a 1 in the denominator (that cancels out):

(2 * 10⁸ * 10⁴) / (10^-7 * 10^-5)

 

When we multiply base numbers with exponents, we can add the exponents together:

8 + 4 = 12

-7 + (-5) = -12

Giving us:

(2 * 10¹²) / (10^-12)

 

When we divide base numbers with exponents, we subtract:

12 - (-12) = 24

Giving us with the final answer of:

2 * 10²⁴