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 next set of problems: 8. Write 0.416 666 667 correct to 3 significant figures. Step 1: Identify the first three significant figures. The first non-zero digit is 4, so it is the first significant figure. The first three significant figures are 4, 1, and 6. Step 2: Look at the fourth significant figure to determine rounding. The fourth significant figure is 6. Step 3: Round the third significant figure. Since the fourth significant figure (6) is 5 or greater, round up the third significant figure (6) by adding 1 to it. 0.416 → 0.417 Answer: Correct to 3 significant figures, the number is 0.417. 9. Express 12 000 in Standard form. Step 1: Place the decimal point after the first non-zero digit to get a number between 1 and 10. For 12 000, the decimal point is implicitly at the end (12000.). Moving it to get 1.2. Step 2: Count how many places the decimal point was moved. The decimal point moved 4 places to the left (from after the last 0 to between 1 and 2). Step 3: Write the number in standard form a × 10^n. Since the original number is greater than 1, the exponent n is positive. 1.2 × 10^4 Answer: 12 000 in standard form is 1.2 × 10^4. 10. Write 2.36 × 10^-3 as a decimal number (ordinary form). Step 1: Identify the exponent of 10. The exponent is -3. This means the decimal point needs to be moved 3 places to the left. Step 2: Move the decimal point. Starting with 2.36, move the decimal point 3 places to the left, adding zeros as placeholders. 2.36 → 0.236 → 0.0236 → 0.00236 Answer: 2.36 × 10^-3 as a decimal number is 0.00236. 11. How many significant figures are in 10.659 22? Step 1: Apply the rules for significant figures. • All non-zero digits are significant (1, 6, 5, 9, 2, 2). There are 6 such digits. • Zeros between non-zero digits are significant. The zero between 1 and 6 is significant. There is 1 such digit. Step 2: Count the total number of significant figures. Total significant figures = 6 (non-zero digits) + 1 (trapped zero) = 7. Answer: The number 10.659 22 has 7 significant figures. What's next?