Place Value & Powers of 10 — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
3,450,000 is less than 3,045,000 because 45 is less than 45.
Corrected: 3,450,000 is greater than 3,045,000 because the hundred-thousands digit 4 is greater than the 0 in 3,045,000.
The corrected sentence is: "3,450,000 is greater than 3,045,000 because the hundred-thousands digit 4 is greater than the 0 in 3,045,000." The error was incorrect comparison: the original sentence "3,450,000 is less than 3,045,000 because 45 is less than 45." needed to be fixed.
2. Fix the sentence:
When you multiply 56 by 10, the digits shift one place to the left and you get 5,600.
Corrected: When you multiply 56 by 10, the digits shift one place to the left and you get 560, not 5,600.
The corrected sentence is: "When you multiply 56 by 10, the digits shift one place to the left and you get 560, not 5,600." The error was wrong shift count: the original sentence "When you multiply 56 by 10, the digits shift one place to the left and you get 5,600." needed to be fixed.
3. Fix the sentence:
The number 8,200,000 has a 2 in the ten-thousands place.
Corrected: The number 8,200,000 has a 2 in the hundred-thousands place, not the ten-thousands place.
The corrected sentence is: "The number 8,200,000 has a 2 in the hundred-thousands place, not the ten-thousands place." The error was place value misidentification: the original sentence "The number 8,200,000 has a 2 in the ten-thousands place." needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. Compare using >, <, or =: 5,320,000 > 5,302,000.
Both numbers have 5 in the millions place and 3 in the hundred-thousands place, but 5,320,000 has a 2 in the ten-thousands place while 5,302,000 has a 0, so 5,320,000 is greater.
2. Order from least to greatest: 740,000 ; 704,000 ; 7,400,000. Answer: 704,000 ; 740,000 ; 7,400,000.
704,000 is the smallest because it has 0 ten-thousands, 740,000 is next with 4 ten-thousands, and 7,400,000 is the largest because it is in the millions.
3. The digit 6 in 1,600,000 is worth 100 times the digit 6 in 16,000.
The 6 in 1,600,000 is in the hundred-thousands place (600,000) and the 6 in 16,000 is in the thousands place (6,000). Since 600,000 ÷ 6,000 = 100, it is 100 times greater.
4. In the number 9,085,400 the digit in the millions place is 9.
The millions place is the leftmost digit in a 7-digit number, so the 9 in 9,085,400 represents 9,000,000.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Which is greater, 2,950,000 or 2,590,000? Explain how you decided by looking at the digits.
Sample answer: 2,950,000 is greater. Both have 2 in the millions place, but 9 hundred-thousands is greater than 5 hundred-thousands.
A good answer includes: 2,950,000 is greater. Both have 2 in the millions place, but 9 hundred-thousands is greater than 5 hundred-thousands.
2. The digit 5 appears in both 5,000 and 500,000. How many times greater is the value of the 5 in 500,000 than in 5,000? Show your reasoning.
Sample answer: The 5 in 500,000 is worth 500,000 and the 5 in 5,000 is worth 5,000. 500,000 ÷ 5,000 = 100, so it is 100 times greater.
A good answer includes: The 5 in 500,000 is worth 500,000 and the 5 in 5,000 is worth 5,000. 500,000 ÷ 5,000 = 100, so it is 100 times greater.