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:
345,678 < 345,578 because 5 comes before 6.
Corrected: 345,678 > 345,578 because the hundreds digit 6 is greater than 5 when all other places are equal.
The corrected sentence is: "345,678 > 345,578 because the hundreds digit 6 is greater than 5 when all other places are equal.". The original sentence "345,678 < 345,578 because 5 comes before 6." contained an error that needed to be fixed.
2. Fix the sentence:
980,000 > 1,200,000 because 9 is greater than 1.
Corrected: 1,200,000 > 980,000 because 1.2 million is greater than 980 thousand. Compare the number of digits first.
The corrected sentence is: "1,200,000 > 980,000 because 1.2 million is greater than 980 thousand. Compare the number of digits first.". The original sentence "980,000 > 1,200,000 because 9 is greater than 1." contained an error that needed to be fixed.
3. Fix the sentence:
506,430 = 506,440 because both start with 506.
Corrected: 506,430 < 506,440 because the tens digit 3 is less than 4.
The corrected sentence is: "506,430 < 506,440 because the tens digit 3 is less than 4.". The original sentence "506,430 = 506,440 because both start with 506." contained an error that needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. Compare: 728,415 < 728,451 (write < , > , or =)
Both numbers match through the hundreds place (728,4__). Compare tens: 1 < 5, so 728,415 < 728,451.
2. Compare: 1,350,000 > 1,305,000 (write < , > , or =)
Compare ten-thousands place: 5 > 0, so 1,350,000 > 1,305,000.
3. The greatest 6-digit number using digits 3, 7, 1, 9, 5, 0 is 975,310
To form the greatest number, arrange digits from largest to smallest: 9, 7, 5, 3, 1, 0 → 975,310.
4. Order from least to greatest: 450,200 and 405,200. The smaller number is 405,200
Compare ten-thousands: 450,200 has 5, 405,200 has 0. Since 0 < 5, 405,200 is smaller.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Explain how to compare two 6-digit numbers step by step.
Sample answer: Start from the leftmost digit and compare each place value moving right. The first place where the digits differ tells you which number is greater.
Comparison moves left to right. The first position where digits differ determines the greater number.
2. Why is 999,999 less than 1,000,000 even though it has more non-zero digits?
Sample answer: 1,000,000 has seven digits while 999,999 has only six digits. A number with more digits is always greater when comparing whole numbers.
The number of digits determines overall magnitude. Any 7-digit number is greater than any 6-digit number.