Place Value and Rounding — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
2,748 rounded to the nearest hundred is 2,800.
Corrected: 2,748 rounded to the nearest hundred is 2,700 because the tens digit 4 is less than 5.
The corrected sentence is: "2,748 rounded to the nearest hundred is 2,700 because the tens digit 4 is less than 5." The error was wrong rounding direction: the original sentence "2,748 rounded to the nearest hundred is 2,800." needed to be fixed.
2. Fix the sentence:
In 6,305,412, the digit 0 has a value of 0 because it is not important.
Corrected: In 6,305,412, the digit 0 is a placeholder in the ten-thousands place. It holds that position so all other digits keep their correct values.
The corrected sentence is: "In 6,305,412, the digit 0 is a placeholder in the ten-thousands place. It holds that position so all other digits keep their correct values." The error was misunderstanding of zero as placeholder: the original sentence "In 6,305,412, the digit 0 has a value of 0 because it is not important." needed to be fixed.
3. Fix the sentence:
67,550 rounded to the nearest thousand is 67,000.
Corrected: 67,550 rounded to the nearest thousand is 68,000 because the hundreds digit 5 means we round up.
The corrected sentence is: "67,550 rounded to the nearest thousand is 68,000 because the hundreds digit 5 means we round up." The error was wrong rounding direction: the original sentence "67,550 rounded to the nearest thousand is 67,000." needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. 3,862 rounded to the nearest ten is 3,860
Look at the ones digit, which is 2. Since 2 is less than 5, the tens digit stays at 6, so 3,862 rounds down to 3,860.
2. In 1,450,728, the digit 4 has a value of 400,000
The digit 4 is in the hundred-thousands place, so its value is 4 x 100,000 = 400,000.
3. 125,340 rounded to the nearest thousand is 125,000
The hundreds digit is 3, which is less than 5, so the thousands digit stays at 5 and 125,340 rounds down to 125,000.
4. The digit in the hundred-thousands place of 8,241,506 is 2
Counting from the right, the hundred-thousands place is the sixth position. In 8,241,506, the digit in that spot is 2.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Explain why 4,500 rounds to 5,000 when rounding to the nearest thousand.
Sample answer: When the hundreds digit is exactly 5, the rule is to round up. Since the 5 is in the hundreds place, 4,500 rounds up to 5,000.
A good answer includes: When the hundreds digit is exactly 5, the rule is to round up. Since the 5 is in the hundreds place, 4,500 rounds up to 5,000.
2. A number rounded to the nearest hundred is 6,300. Give one example of a number it could be and one it could not be. Explain why.
Sample answer: It could be 6,280 because that is closer to 6,300 than to 6,200. It could not be 6,360 because that rounds up to 6,400.
A good answer includes: It could be 6,280 because that is closer to 6,300 than to 6,200. It could not be 6,360 because that rounds up to 6,400.