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 of the digit

Using the Place Value knowledge point

$$ \text{In } 36,803, \text{ the digit } 8 \text{ is in the hundreds place, representing } 800. $$

Calculate the change in value

Using the Place Value knowledge point

$$ \text{Replacing } 8 \text{ with } 2 \text{ gives } 36,203. \text{ The digit } 2 \text{ represents } 200. $$

$$ 800 - 200 = 600 $$

$$ \text{Since } 36,203 < 36,803, \text{ the value decreases by } 600. $$

List the number of books

Using the Comparing Numbers knowledge point

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Compare and order the values

Using the Comparing Numbers knowledge point

$$ 462 > 421 > 412 > 375 $$

Identify the second greatest value

Using the Comparing Numbers knowledge point

$$ \text{The greatest is } 462 \text{ (8th grade). The second greatest is } 421 \text{ (6th grade).} $$

Answer:

Question 14

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

Question 15

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