1. Problem: Round 86,999,732 to the nearest thousand. Step 1: Identify the place value to round to, which is the thousand's place (the 4th digit from the right). Step 2: Look at the digit to the right of the thousand's place (the hundreds place). Step 3: If this digit is 5 or more, round up. If less than 5, round down. Step 4: The digit in the thousand's place is 9, and the digit to the right is 7 (which is greater than 5), so we round up. Step 5: Rounding up 9 in the thousand's place causes a carryover: $$86,999,732 \to 87,000,000$$ 2. Problem: Round 1,356.6531 to the nearest hundred. Step 1: Identify the hundred's place (3rd digit from the left). Step 2: Look at the digit to the right (the tens place). Step 3: The hundred's place digit is 3, the tens place digit is 5 (equal to 5), so round up. Step 4: Adding 1 to 3 gives 4, and digits to the right become zero: $$1,356.6531 \to 1,400$$ 3. Problem: Round 498.0539 to the nearest ten. Step 1: Identify the ten's place (2nd digit from the left). Step 2: Look at the digit to the right (the one's place). Step 3: The ten's place digit is 9, the one's place digit is 8 (greater than 5), so round up. Step 4: Adding 1 to 9 causes a carryover: $$498.0539 \to 500$$ 4. Problem: Round 2.11832 to the nearest hundredth. Step 1: Identify the hundredth place (2nd digit after decimal). Step 2: Look at the digit to the right (thousandth place). Step 3: The hundredth digit is 1, the thousandth digit is 8 (greater than 5), so round up. Step 4: Adding 1 to 1 gives 2: $$2.11832 \to 2.12$$ 5. Problem: Round 16.984 to the nearest tenth. Step 1: Identify the tenth place (1st digit after decimal). Step 2: Look at the digit to the right (hundredth place). Step 3: The tenth digit is 9, the hundredth digit is 8 (greater than 5), so round up. Step 4: Adding 1 to 9 causes carryover: $$16.984 \to 17.0$$ 6. Problem: Round 3.00992 to the nearest thousandth. Step 1: Identify the thousandth place (3rd digit after decimal). Step 2: Look at the digit to the right (ten-thousandth place). Step 3: The thousandth digit is 9, the next digit is 2 (less than 5), so round down. Step 4: Keep the thousandth digit as is: $$3.00992 \to 3.010$$ 7. Problem: Round 84,100.52173 to the nearest thousandth. Step 1: Identify the thousandth place (3rd digit after decimal). Step 2: Look at the digit to the right (ten-thousandth place). Step 3: The thousandth digit is 1, the next digit is 7 (greater than 5), so round up. Step 4: Adding 1 to 1 gives 2: $$84,100.52173 \to 84,100.522$$ 8. Problem: Round 935.0894 to the nearest tenth. Step 1: Identify the tenth place (1st digit after decimal). Step 2: Look at the digit to the right (hundredth place). Step 3: The tenth digit is 0, the hundredth digit is 8 (greater than 5), so round up. Step 4: Adding 1 to 0 gives 1: $$935.0894 \to 935.1$$