This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
here are the solutions for the standard form problems. 1) Given p = 3.6 × 10^4 and q = 9 × 10^4. a) Find pq Step 1: Multiply the numerical parts and the powers of 10 separately. pq = (3.6 × 10^4) × (9 × 10^4) pq = (3.6 × 9) × (10^4 × 10^4) Step 2: Perform the multiplication and apply the exponent rule a^m × a^n = a^m+n. pq = 32.4 × 10^4+4 pq = 32.4 × 10^8 Step 3: Convert the result to standard form (a number between 1 and 10 multiplied by a power of 10). 32.4 = 3.24 × 10^1 pq = (3.24 × 10^1) × 10^8 pq = 3.24 × 10^1+8 pq = 3.24 × 10^9 b) Find (p)/(q) Step 1: Divide the numerical parts and the powers of 10 separately. (p)/(q) = (3.6 × 10^4)/(9 × 10^4) (p)/(q) = ((3.6)/(9)) × ((10^4)/(10^4)) Step 2: Perform the division and apply the exponent rule (a^m)/(a^n) = a^m-n. (p)/(q) = 0.4 × 10^4-4 (p)/(q) = 0.4 × 10^0 (p)/(q) = 0.4 × 1 (p)/(q) = 0.4 Step 3: Convert the result to standard form. 0.4 = 4 × 10^-1 (p)/(q) = 4 × 10^-1 2) Given m = 2 × 10^3 and n = 5 × 10. Note that n = 5 × 10^1. a) Find mn Step 1: Multiply the numerical parts and the powers of 10 separately. mn = (2 × 10^3) × (5 × 10^1) mn = (2 × 5) × (10^3 × 10^1) Step 2: Perform the multiplication and apply the exponent rule a^m × a^n = a^m+n. mn = 10 × 10^3+1 mn = 10 × 10^4 Step 3: Convert the result to standard form. 10 = 1 × 10^1 mn = (1 × 10^1) × 10^4 mn = 1 × 10^1+4 mn = 1 × 10^5 b) Find (n)/(m) Step 1: Divide the numerical parts and the powers of 10 separately. (n)/(m) = (5 × 10^1)/(2 × 10^3) (n)/(m) = ((5)/(2)) × ((10^1)/(10^3)) Step 2: Perform the division and apply the exponent rule (a^m)/(a^n) = a^m-n. (n)/(m) = 2.5 × 10^1-3 (n)/(m) = 2.5 × 10^-2 This result is already in standard form. (n)/(m) = 2.5 × 10^-2 What's next?