Question

word problems!
directions: answer the following questions in complete sentences. show all of your work neatly in the space provided, and write your final answer in a complete sentence. do not leave any questions blank!

1. **in the number 36,803, if the 8 was replaced with a 2, would the value increase or decrease? what would the change in value be?
2. north star wants to know how many books are in the libraries. we learn that there are 412 books in the 5th grade library, 421 in the 6th grade, 375 in the 7th grade and 462 in the 8th grade. which grade has the second greatest number of books?

Explanation:

Identify place value change

Using the Place Value knowledge point:

• Original number: \(36,803\)
• New number: \(36,203\)
• The digit \(8\) in the hundreds place is replaced by \(2\).

Calculate value difference

Using the Place Value knowledge point:

• Original value of hundreds place: \(8 \times 100 = 800\)
• New value of hundreds place: \(2 \times 100 = 200\)
• Since \(200 < 800\), the value decreases.
• Change in value: \(800 - 200 = 600\)

List and order library books

• \(5^{\text{th}}\) grade: \(412\) books
• \(6^{\text{th}}\) grade: \(421\) books
• \(7^{\text{th}}\) grade: \(375\) books
• \(8^{\text{th}}\) grade: \(462\) books
• Ordering from greatest to least: \(462 > 421 > 412 > 375\)

Determine second greatest value

• Greatest number of books: \(462\) (\(8^{\text{th}}\) grade)
• Second greatest number of books: \(421\) (\(6^{\text{th}}\) grade)

Answer:

Question 14

If the 8 was replaced with a 2, the value would decrease. The change in value would be 600.

Question 15

The 6th grade has the second greatest number of books.