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.
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You're on a roll — here are the solutions to the problems. THURSDAY 1. Express the following numbers into standard form: Standard form (or scientific notation) is written as a × 10^n, where 1 |a| < 10 and n is an integer. a) 3293.02 Step 1: Move the decimal point to the left until there is only one non-zero digit before it. 3293.02 3.29302 Step 2: Count how many places the decimal point was moved. It was moved 3 places to the left, so the exponent n is 3. The standard form is 3.29302 × 10^3. b) 0.00342 Step 1: Move the decimal point to the right until there is only one non-zero digit before it. 0.00342 3.42 Step 2: Count how many places the decimal point was moved. It was moved 3 places to the right, so the exponent n is -3. The standard form is 3.42 × 10^-3. c) 0.284 Step 1: Move the decimal point to the right until there is only one non-zero digit before it. 0.284 2.84 Step 2: Count how many places the decimal point was moved. It was moved 1 place to the right, so the exponent n is -1. The standard form is 2.84 × 10^-1. d) 397203 Step 1: Assume the decimal point is at the end of the number (397203.). Move it to the left until there is only one non-zero digit before it. 397203 3.97203 Step 2: Count how many places the decimal point was moved. It was moved 5 places to the left, so the exponent n is 5. The standard form is 3.97203 × 10^5. 2. Write the numbers whose standard form is: To convert from standard form to an ordinary number, move the decimal point according to the exponent of 10. A positive exponent means moving right, and a negative exponent means moving left. a) 3.5764 × 10^3 Step 1: The exponent is 3, so move the decimal point 3 places to the right. 3.5764 3576.4 The number is 3576.4. b) 9.3816 × 10^3 Step 1: The exponent is 3, so move the decimal point 3 places to the right. 9.3816 9381.6 The number is 9381.6. c) 9.002 × 10^5 Step 1: The exponent is 5, so move the decimal point 5 places to the right. Add zeros as needed. 9.002 900200 The number is 900200. 3. Use a calculator to find the square root of: a) 483.93 Step 1: Use a calculator to find the square root of 483.93. sqrt(483.93) ≈ 21.9984089... Step 2: Round to a suitable number of decimal places (e.g., 3 decimal places). The square root is approximately 21.998. b) 294.3 Step 1: Use a calculator to find the square root of 294.3. sqrt(294.3) ≈ 17.155174... Step 2: Round to a suitable number of decimal places (e.g., 3 decimal places). The square root is approximately 17.155. Got more? Send 'em!