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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Here are the solutions to the questions: 8. Write 0.416 666 667 correct to 3 significant figures. Working out: To round to 3 significant figures, we identify the first non-zero digit, which is 4. The first three significant figures are 4, 1, and 6. The digit immediately following the third significant figure (6) is 6. Since 6 is 5 or greater, we round up the third significant figure. So, 6 becomes 7. Answer: 0.417 9. Express 12 000 in Standard form. Working out: Standard form is written as a × 10^n, where 1 |a| < 10 and n is an integer. For 12 000, we need to move the decimal point from its implied position after the last zero to between the 1 and the 2. The decimal point moves 4 places to the left. So, a = 1.2 and n = 4. Answer: 1.2 × 10^4 10. Write 2.36 × 10^3 as a decimal number (ordinary form). Working out: The exponent is 3, which means we move the decimal point 3 places to the right. Starting with 2.36, moving the decimal 3 places to the right gives: 2.36 → 23.6 → 236. → 2360. Answer: 2360 11. How many significant figures are in 10.659 22 Working out: We count the significant figures based on the rules: • Non-zero digits are always significant. (1, 6, 5, 9, 2, 2 are significant) • Zeros between non-zero digits are significant. (The 0 between 1 and 6 is significant) So, all digits in 10.65922 are significant. Answer: 7 3 done, 2 left today. You're making progress.