Estimation and Rounding — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
Rounded to the nearest hundred, 12,345 is 12,400.
Corrected: Rounded to the nearest hundred, 12,345 is 12,300.
The tens digit determines rounding to the hundreds place. Since 4 is less than 5, we round down to 12,300.
2. Fix the sentence:
Rounded to the nearest thousand, 12,345 is 13,000.
Corrected: Rounded to the nearest thousand, 12,345 is 12,000.
Rounding to the nearest thousand uses the hundreds digit. Since 3 is less than 5, we round down to 12,000.
3. Fix the sentence:
Rounded to the nearest ten thousand, 12,345 is 20,000.
Corrected: Rounded to the nearest ten thousand, 12,345 is 10,000.
Rounding to the nearest ten thousand uses the thousands digit. Since 2 is less than 5, we round down to 10,000.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. Rounded to the nearest hundred, 47,682 is 47,700.
Since the tens digit (8) is 5 or greater, we round the hundreds place up to 47,700.
2. Rounded to the nearest thousand, 47,682 is 48,000.
The hundreds digit is 6, which is greater than 5, so 47,682 rounds up to 48,000.
3. Rounded to the nearest ten thousand, 47,682 is 50,000.
The thousands digit is 7, which is 5 or greater, so we round up to 50,000.
4. Rounded to the nearest hundred thousand, 354,128 is 400,000.
The ten-thousands digit is 5, so we round up to the next hundred thousand, giving 400,000.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Round 26,789 to the nearest hundred, thousand, and ten thousand. Show each result.
Sample answer: Nearest hundred: 26,800 (tens digit 8 rounds up). Nearest thousand: 27,000 (hundreds digit 7 rounds up). Nearest ten thousand: 30,000 (thousands digit 6 rounds up).
Each rounding looks at the next-smaller place: 8, 7, and 6 are each 5 or greater, so all three round up.
2. A town has 89,453 people. Round this to the nearest hundred and to the nearest ten thousand. Compare your two answers.
Sample answer: Nearest hundred: 89,500 (tens digit 5 rounds up). Nearest ten thousand: 90,000 (thousands digit 9 rounds up). The ten-thousand estimate is less precise but easier to remember.
Rounding to a smaller place keeps more detail, while rounding to a larger place gives a simpler approximate value.