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 to the problems on standard form. 1) Write the following in standard form: a) 0.032 Step 1: Move the decimal point to the right until there is one non-zero digit to its left. 0.032 3.2 Step 2: Count how many places the decimal point moved. It moved 2 places to the right, so the exponent of 10 is -2. 0.032 = 3.2 × 10^-2 b) 67000 Step 1: Move the decimal point to the left until there is one non-zero digit to its left. 67000 6.7 Step 2: Count how many places the decimal point moved. It moved 4 places to the left, so the exponent of 10 is 4. 67000 = 6.7 × 10^4 2) Simplify the following, leaving your answers in standard form: a) 2.6 × 10^4 + 1.3 × 10^3 Step 1: Make the powers of 10 the same. Convert 1.3 × 10^3 to a term with 10^4. 1.3 × 10^3 = 0.13 × 10^4 Step 2: Add the coefficients. 2.6 × 10^4 + 0.13 × 10^4 = (2.6 + 0.13) × 10^4 = 2.73 × 10^4 Step 3: Ensure the answer is in standard form. 2.73 is between 1 and 10, so it is in standard form. 2.73 × 10^4 b) 6.4 × 10^-2 + 5.5 × 10^-2 Step 1: The powers of 10 are already the same (10^-2). Add the coefficients. (6.4 + 5.5) × 10^-2 = 11.9 × 10^-2 Step 2: Convert the result to standard form. 11.9 is not between 1 and 10. 11.9 × 10^-2 = (1.19 × 10^1) × 10^-2 = 1.19 × 10^1-2 = 1.19 × 10^-1 1.19 × 10^-1 c) 7.52 × 10^-3 - 2.5 × 10^-3 Step 1: The powers of 10 are already the same (10^-3). Subtract the coefficients. (7.52 - 2.5) × 10^-3 = 5.02 × 10^-3 Step 2: Ensure the answer is in standard form. 5.02 is between 1 and 10, so it is in standard form. 5.02 × 10^-3 That's 2 down. 3 left today — send the next one.