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 problems: 11. Name the place value to which 16.932 was rounded to 20. Step 1: Compare the original number 16.932 with the rounded number 20. Step 2: The number was rounded to the nearest whole number, specifically to the tens place, as 16.932 is closer to 20 than to 10. The digit in the tens place is 1, and the digit to its right is 6. Since 6 5, the tens digit is rounded up to 2, and all subsequent digits become 0. The place value is the tens place. 12. Name the place value to which 0.581 was rounded to 0.58. Step 1: Compare the original number 0.581 with the rounded number 0.58. Step 2: The number was rounded to two decimal places, which is the hundredths place. The digit in the hundredths place is 8, and the digit to its right is 1. Since 1 < 5, the hundredths digit is kept as it is. The place value is the hundredths place. 13. Name the place value to which 7.429 was rounded to 7.4. Step 1: Compare the original number 7.429 with the rounded number 7.4. Step 2: The number was rounded to one decimal place, which is the tenths place. The digit in the tenths place is 4, and the digit to its right is 2. Since 2 < 5, the tenths digit is kept as it is. The place value is the tenths place. 14. Estimate Round to the nearest tenth. Step 1: Observe the position of on the number line. It is between 5.6 and 5.65. Step 2: To round to the nearest tenth, we look at the hundredths digit. Any number less than 5.65 will round down to 5.6. The rounded value of to the nearest tenth is 5.6. 15. The area of a campground is exactly halfway between 25.9 acres and 26 acres. What is the area of the campground? Step 1: To find the number exactly halfway between two numbers, calculate their average. Step 2: Add the two numbers and divide by 2. Area = (25.9 + 26)/(2) Area = (51.9)/(2) Area = 25.95 acres 16. Model Real Life What is the greatest weight rounded to the nearest tenth? The weights are 0.592 kg, 0.605 kg, 0.694 kg, 0.547 kg. Step 1: Round each weight to the nearest tenth. • 0.592 kg: The tenths digit is 5. The next digit is 9. Since 9 5, round up 5 to 6. → 0.6 kg • 0.605 kg: The tenths digit is 6. The next digit is 0. Since 0 < 5, keep 6. → 0.6 kg • 0.694 kg: The tenths digit is 6. The next digit is 9. Since 9 5, round up 6 to 7. → 0.7 kg • 0.547 kg: The tenths digit is 5. The next digit is 4. Since 4 < 5, keep 5. → 0.5 kg Step 2: Compare the rounded values: 0.6 kg, 0.6 kg, 0.7 kg, 0.5 kg. The greatest weight rounded to the nearest tenth is 0.7 kg. 17. Model Real Life What is the least weight rounded to the nearest hundredth? The weights are 0.592 kg, 0.605 kg, 0.694 kg, 0.547 kg. Step 1: Round each weight to the nearest hundredth. • 0.592 kg: The hundredths digit is 9. The next digit is 2. Since 2 < 5, keep 9. → 0.59 kg • 0.605 kg: The hundredths digit is 0. The next digit is 5. Since 5 5, round up 0 to 1. → 0.61 kg • 0.694 kg: The hundredths digit is 9. The next digit is 4. Since 4 < 5, keep 9. → 0.69 kg • 0.547 kg: The hundredths digit is 4. The next digit is 7. Since 7 5, round up 4 to 5. → 0.55 kg Step 2: Compare the rounded values: 0.59 kg, 0.61 kg, 0.69 kg, 0.55 kg. The least weight rounded to the nearest hundredth is 0.55 kg. 18. DIG DEEPER Round each weight to the nearest tenth. Which rounded value is closest to its recorded value? Which rounded value is farthest from its recorded value? The weights are 0.592 kg, 0.605 kg, 0.694 kg, 0.547 kg. Step 1: Round each weight to the nearest tenth (from problem 16). • 0.592 kg → 0.6 kg • 0.605 kg → 0.6 kg • 0.694 kg → 0.7 kg • 0.547 kg → 0.5 kg Step 2: Calculate the absolute difference between the original and rounded values. • For 0.592 kg: |0.592 - 0.6| = |-0.008| = 0.008 • For 0.605 kg: |0.605 - 0.6| = |0.005| = 0.005 • For 0.694 kg: |0.694 - 0.7| = |-0.006| = 0.006 • For 0.547 kg: |0.547 - 0.5| = |0.047| = 0.047 Step 3: Identify the smallest and largest differences. The smallest difference is 0.005, so 0.605 kg rounded to 0.6 kg is the closest. The largest difference is 0.047, so 0.547 kg rounded to 0.5 kg is the farthest. 19. Find the product. 7 × 40 = Step 1: Multiply the non-zero digits. 7 × 4 = 28 Step 2: Add the zero from 40. 7 × 40 = 280 20. Find the product. 5,000 × 9 = Step 1: Multiply the non-zero digits. 5 × 9 = 45 Step 2: Add the three zeros from 5,000. 5,000 × 9 = 45,000 21. Find the product. 8 × 200 = Step 1: Multiply the non-zero digits. 8 × 2 = 16 Step 2: Add the two zeros from 200. 8 × 200 = 1,600 What's next?