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Lesson Plans and Worksheets for Grade 8

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 8

Common Core For Grade 8

Examples, videos, and solutions to help Grade 8 students learn how to compare numbers expressed in scientific notation.

### New York State Common Core Math Module 1, Grade 8, Lesson 13

Worksheets and solutions for Common Core Grade 8, Module 1, Lesson 13

### Lesson 13 Student Outcomes

• Students compare numbers expressed in scientific notation.

• Students apply the laws of exponents to interpret data and use technology to compute with very large numbers.

Lesson 13 Summary

• Students have completed the lessons on exponential notation, the properties of integer exponents, magnitude, and scientific notation.

• Students can read, write, and operate with numbers expressed in scientific notation, which is the language of many sciences. Additionally, they can interpret data using technology.

Classwork

Example 1

Among the galaxies closest to Earth, M82 is about 1.15 x 10^{7} light-years away and Leo I Dwarf is about 8.2 x 10^{5} light-years away.
Which is closer?

Exercise 1

The Fornax Dwarf galaxy is 4.6 x 10^{5} light-years away from Earth, while Andromeda I is 2.430 x 10^{6} light-years away
from Earth. Which is closer to Earth?

Exercise 2

The average lifetime of the tau lepton 2.906 x 10^{-13} is seconds and the average lifetime of the neutral pion is 8.4 x 10^{-17}
seconds. Explain which subatomic particle has a longer average lifetime.

Exploratory Challenge 1/Exercise 3

Theorem: Given two numbers in scientific notation, a x 10^{m} and b x 10^{n}, if m < n, then a x 10^{m} < b x 10^{n}

Example 3

Compare 1.815 x 10^{14} and 1.82 x 10^{14}

Exercise 4

Compare 9.3 x 10^{28} and 9.2879 x 10^{28}

Exercise 5

Chris said 5.3 x 10^{41} < 5.301 x 10^{28} that because 5.3 has fewer digits than 5.301. Show that even though his answer
is correct, his reasoning is flawed. Show him an example to illustrate that his reasoning would result in an incorrect
answer. Explain.

Exploratory Challenge 2/Exercise 6

You have been asked to determine the exact number of Google searches that are made each year. The only information you are provided is that there are 35,939,938,877 searches performed each week. Assuming the exact same number of searches is performed each week for the 52 weeks in a year, how many total searches will have been performed in one year? Your calculator does not display enough digits to get the exact answer. Therefore, you must break down the problem into smaller parts. Remember, you cannot approximate an answer because you need to find an exact answer. Use the screen shots below to help you reach your answer.

Yahoo is another popular search engine. Yahoo receives requests for 1,792,671,335 searches each month. Assuming the same number of searches is performed each month, how many searches are performed on Yahoo each year? Use the screen shots below to help determine the answer.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Lesson Plans and Worksheets for Grade 8

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 8

Common Core For Grade 8

Examples, videos, and solutions to help Grade 8 students learn how to compare numbers expressed in scientific notation.

• Students apply the laws of exponents to interpret data and use technology to compute with very large numbers.

Lesson 13 Summary

• Students have completed the lessons on exponential notation, the properties of integer exponents, magnitude, and scientific notation.

• Students can read, write, and operate with numbers expressed in scientific notation, which is the language of many sciences. Additionally, they can interpret data using technology.

Classwork

Example 1

Among the galaxies closest to Earth, M82 is about 1.15 x 10

Exercise 1

The Fornax Dwarf galaxy is 4.6 x 10

Exercise 2

The average lifetime of the tau lepton 2.906 x 10

Exploratory Challenge 1/Exercise 3

Theorem: Given two numbers in scientific notation, a x 10

Example 3

Compare 1.815 x 10

Exercise 4

Compare 9.3 x 10

Exercise 5

Chris said 5.3 x 10

Exploratory Challenge 2/Exercise 6

You have been asked to determine the exact number of Google searches that are made each year. The only information you are provided is that there are 35,939,938,877 searches performed each week. Assuming the exact same number of searches is performed each week for the 52 weeks in a year, how many total searches will have been performed in one year? Your calculator does not display enough digits to get the exact answer. Therefore, you must break down the problem into smaller parts. Remember, you cannot approximate an answer because you need to find an exact answer. Use the screen shots below to help you reach your answer.

Yahoo is another popular search engine. Yahoo receives requests for 1,792,671,335 searches each month. Assuming the same number of searches is performed each month, how many searches are performed on Yahoo each year? Use the screen shots below to help determine the answer.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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