# Lesson 3 Problem Set 5.1 Answer Key

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Are you looking for Lesson 3 Problem Set 5.1 Answer Key for NYS Common Core Mathematics Curriculum Engage NY? If so, here you may be able to find the answer so that you are able to make sure whether your answer is correct or not. Let’s find out the answer key below.

Answer Key of Lesson 3 Problem Set 5.1

This key answer can be found in this link here. Cited from that link, here is the key answer for Lesson 3 Problem Set 5.1.

1. In the number one, you are required to write the following in exponential form (e.g., 100 = 102)

a. 10,000 = 104
b. 1000 = 103
c. 10 x 10 = 102
d. 100 x 100 = 104
e. 1,000,000 = 106
f. 1000 x 1000 = 106

2. In the number two, you are required to write the following in standard form, for example 5 x 102= 500

a. 9 x 103 = 9,000
b. 39 x 104= 390,000
c. 7200 : 102 = 72
d. 7,200,000 : 103 = 7,200
e. 4.025 x 103 = 4,025
f. 40.25 x 104 = 402,500
g. 725 : 103 = 0.725
h. 7.2 : 102 = 0.72

3. In this number, you have to think about the answers to Problem 2 (a-d). You are required to explain the pattern used to find an answer when you multiply or divide a whole number by a power of 10.

Answer: When multiplying by a power of 10, I add zeros onto my whole number that equals my exponent. When dividing by a power of 10, I subtract zeros from my whole number that equals my exponent.

4. In this number, you are required to think about the answers to Problem 2(e-h). You have to be able to give your explanation about the pattern which is used to place the decimal in the answer when you multiply or divide a decimal by a power of 1.

Answer: When multiplying by a power of 10, the decimal point is moved to the right equal to my exponent to make my answer larger. When dividing by a power of 10, the decimal point is moved to the left equal to my exponent to make my answer smaller.

5. In this number, you are required to complete the patterns.

a. 0.03 0.3 3.0 300 3000
b. 6,500,000 65,000 650 6.5 0.065
c. 94,300 9,430 943 94.3 9.43 0.943
d. 999 9990 99,900 999,000 9,990,000 99,900,000
e. 0.075 7.5 750 75,000 7,500,000 750,000,000
f. Here, you are required to explain how you found the missing numbers in set b and you have to make sure that you include your reasoning about the number of zeros in your numbers and how you placed the decimal.
Answer: The next number in the pattern had 2 zeros less, so the numbers were being divided by 102 which makes it smaller by 2 places.
g. Here, you are required to explain how you found the missing numbers in set d and you have to make sure that you give your reasoning about the number of zeros in your numbers and how you put the decimal.
Answer: The whole numbers added one zero, so the numbers were being multiplied by 101 which makes it larger by one place or column each time in the pattern.

6. In this number, there is a story where Shauunie and Marlon missed the lesson on exponents and then Shaunnie incorrectly wrote 105 = 50 on her paper, and Marlon mistakenly wrote 2.5 x 102 = 2.500 on his paper.

a. Here, you are asked what mistake that has been made by Shaunnie and you have to explain it using words, numbers and pictures why her thinking is incorrect and what she needs to do to correct the answer that she made.
Answer: Shaunnie thinks 105 is 10 x 5 which is 50, but 105 means 10 x 10 x 10 x 10 x 10 which equals 100,000.

b. Here, you are asked about the mistake that Marlon has made and you have to explain it using words, numbers and pictures why his thinking is not correct and what he needs to do to correct the answer that he made.
Answer: Marlon made the mistake of adding two zeros at the end of 2.5. That would have worked for a whole number, but 2.5 is a decimal so he needs to move the decimal point to the right two shifts making 250.