(2x10^n)+(4.02x10^5), what is n?
Explanation:
To determine the value of n, we need to rewrite the expression as a number in scientific notation, in the form a x 10^n, where 1 ≤ a < 10.
We can start by factoring out 10^n from both terms:
(2 x 10^n) + (4.02 x 10^5) = 10^n (2 + 4.02 x 10^-5)
Now we need to divide both sides of the equation by (2 + 4.02 x 10^-5):
(2 x 10^n) + (4.02 x 10^5) / (2 + 4.02 x 10^-5) = 10^n
We can simplify the expression on the left side by multiplying the numerator and denominator by 10^5:
(2 x 10^n x 10^5 + 4.02 x 10^5) / (2 x 10^5 + 4.02) = 10^n
Simplifying the numerator:
(2 x 10^(n+5) + 4.02 x 10^5) / (2 x 10^5 + 4.02) = 10^n
Now we can cross-multiply to eliminate the fraction:
(2 x 10^(n+5) + 4.02 x 10^5) = 10^n (2 x 10^5 + 4.02)
Expanding both sides:
2 x 10^(n+5) + 4.02 x 10^5 = 2 x 10^(n+5) + 4.02 x 10^n
Subtracting 2 x 10^(n+5) from both sides:
4.02 x 10^5 = 4.02 x 10^n
Dividing both sides by 4.02:
10^5 = 10^n
Therefore, n = 5.