Question 1: What is the place value of the digit 7 in the number 3,784,591,206?

Answer: 700,000,000

Question 2: Identify the mistake in the following statement: 'In 5,432,109,876, the digit 9 is in the thousands place.'

Answer: The 9 is in the ten-thousands place, not thousands.

Question 3: Write the number 7,654,321,098 in expanded form, indicating the place value of each digit.

Answer: 7,000,000,000 + 600,000,000 + 50,000,000 + 4,000,000 + 300,000 + 20,000 + 1,000 + 90 + 8

Question 4: If a student writes 8,345,672,019 and claims the 4 is in the hundreds place, identify the error.

Answer: The 4 is in the ten-millions place, not hundreds.

Question 1: A student says that the digit 3 in the number 2,305,768,491 is in the hundreds place. Is this correct? Explain your reasoning.

Answer: No, the 3 is in the hundreds place in 2,305,768,491 only if counting from the right: units, tens, hundreds. Here, it is in the millions place; the 3 is in the millions place.

Question 2: Construct a number between 1 billion and 2 billion where the digit 5 is in the hundred-millions place. Write it in standard form and expanded form.

Answer: 1,500,000,000; expanded: 1,000,000,000 + 500,000,000

Question 3: Explain why the number 9,876,543,210 might be misinterpreted if someone confuses the place value of the digit 2.

Answer: Because the 2 is in the units place, but some might think it's in the hundreds or thousands if not carefully counting from right to left.

Question 4: Given the number 6,732,009,815, identify the digit in the ten-millions place and its value.

Answer: The digit is 3, and its value is 30,000,000.

Question 1: A bank statement shows a deposit of 9,876,543,210 dollars. A clerk claims the 4 in the number is in the thousands place. Is this correct? Explain.

Answer: No, the 4 is in the hundreds of thousands place, not thousands. The place value depends on position from the right.

Question 2: A company's revenue is listed as 1,234,567,890. An accountant notes that the 7 is in the hundreds place. Verify this claim.

Answer: Incorrect, the 7 is in the millions place, not hundreds.

Question 1: Create a 9-digit number where the digit 6 is in the hundreds of thousands place, and the number is divisible by 9. Write the number and explain how you verified divisibility.

Answer: Example: 3,456,786,921; sum of digits = 3+4+5+6+7+8+6+9+1=49, which is not divisible by 9, so adjust accordingly.

Question 2: Analyze the common misconception: Students often think that the digit 0 has no value. Provide an example with a number up to billions illustrating the importance of zeros in place value.

Answer: Example: 2,045,006,700. Zeros indicate missing units, tens, or hundreds in certain positions, affecting the number's value.

Question 1: Student writes 8,765,432,109 and states the digit 1 is in the thousands place. Is this correct? If not, correct the statement and explain.

Answer: Incorrect. The 1 is in the hundreds place, not thousands. The thousands digit is 2.

Question 2: A student labels the number 9,000,000,001 as having the 9 in the millions place. Is this correct? Clarify your answer.

Answer: Incorrect. The 9 is in the billions place, not millions.