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Scientific Notation Practice (4 Favorites)

ACTIVITY in Measurements, Scientific Notation. Last updated June 25, 2021.


Summary

In this activity, students will learn about the importance of scientific notation to the science community. Through guided practice problems, students will be introduced to scientific notation and learn how to convert values into scientific notation.  

Grade Level

Middle School

NGSS Alignment

This activity will help prepare your students to meet the performance expectations in the following standards:

  • Scientific and Engineering Practices:
    • Using Mathematics and Computational Thinking

Objectives

By the end of this activity, students should be able to

  • Understand why the scientific community needs to use scientific notation.
  • Properly convert both large and small values into scientific notation.

Chemistry Topics

This activity supports students’ understanding of

  • Quantitative Chemistry
  • Scientific Notation
  • Measurement

Time

Teacher Preparation: minimal
Lesson: 20-30 minutes

Materials

  • Student Handout

Safety

  • No specific safety precautions need to be observed for this activity.

Teacher Notes

  • Background:
    • Scientific notation is used to express very large and very small numbers so that problem solving will be quicker and easier. 
    • Mathematicians and scientists can work with very large or small numbers more easily if they are expressed in scientific notation.
  • This short instructional video can be used as a review or for concept reinforcement. 
  • Archimedes discovered Scientific Notation. He was a Greek mathematician and inventor.  Archimedes was asked to calculate the number of grains of sand in the universe. This request is what lead to the discovery of scientific notation.
  • Additional examples of scientific large numbers to share with students:

Planet
Mass (Kg)
Scientific Notation
Jupiter
3,700,000,000,000,000,000,000,000,000
3.7 x 10 ²⁷
Uranus
870,000,000,000,000,000,000,000,000
8.7 x 10²⁵
Neptune
100,000,000,000,000,000,000,000,000
1.0 x 10²⁶
Saturn
5,700,000,000,000,000,000,000,000,000
5.7 x 10²⁶
  • Examples of scientific small numbers to share with students:

Item
Size
Scientific Notation
Organism Mycoplasma laidawii
Diameter
0.000004 inches
4.0 x 10 ˉ⁶
One atom of gold
Mass
0.000000000000000000000327
3.27 x 10 ˉ²²
  • The Student Handout is designed to be used as guided notes first, followed by independent student work.
    • First, I give each student a copy and lead a discussion about “The Rules of Scientific Notation” while they each follow along. I add additional notes that might be helpful.
    • Next, I have students complete the “Guided Practice Problems” independently or with a partner. I use this time to identify if students understand the concept, or if any students need additional assistance. 
    • Students who are ready can then move on to independently complete the “Practice Problems”.  It can be given as classwork or homework.
    • If needed you can provide more practice by using any of the very large or very small numbers from the tables.    
    • The “Challenge” section of the worksheet should be completed once students have mastered the concept of scientific notation.

For the Student

Lesson

Background

Archimedes discovered Scientific Notation. He was a Greek mathematician and inventor.  Archimedes was asked to calculate the number of grains of sand in the universe. This request is what lead to the discovery of scientific notation. His calculation of how many grains of sand? A “one” followed by 63 zeros:

1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Scientific notation is used to express very large and very small numbers so that problem solving will be quicker and easier. Mathematicians and scientists can work with very large or small numbers more easily if they are expressed in scientific notation.

Rules of Scientific Notation

Values that are greater than 1:

  • Move the decimal point to create a number that is greater than or equal to 1 but less than 10. (Tip: Remember that a decimal point exists at the end of a value, even if it isn’t written!)

33100561→ 3.3100561

  • Count the number of times you moved the decimal point (the decimal point originated at the end of the number).

33100561. → 3.3100561
The decimal point was moved 7 times to the left

  • Determine an exponent. This is based on how many factors of 10 the original number was changed. The exponent is the same number of zeros as you moved the decimal place. Since the original value is a large number, larger than 1, the exponent is positive. 

The original number was reduced by a factor of 10000000

  • Convert this factor into a power of ten number. The exponent and the number of zeroes (or places the decimal point was moved) is the same.

10⁷

  • Write the value using scientific notation. To do this write it as a product of two numbers: the “new” number (that is between 1 and 10) and the power number (that is a Power of 10). 

3.3100561 X 10⁷

Values that are less than 1:

  • Move the decimal point to create a number that is greater than or equal to 1 but less than 10.

0.00000033100561  → 3.3100561M

  • Count the number of times you moved the decimal point.

0.00000033100561  → 3.3100561
The decimal point was moved 7 times to the right

  • Determine an exponent. This is based on how many factors of 10 the original number was changed. Since the original value is a small number, smaller than 1, the exponent is negative.

The original number was increased by a factor of 10000000

  • Convert the Power Number into a Power of ten number. The exponent and the number of places the decimal point was moved is the same.

10ˉ

  • Write the value using scientific notation. To do this write it as a product of two numbers: the “new” number (that is between 1 and 10) and the power number (that is a Power of 10). 

3.3100561 X 10ˉ

Guided Practice Problems

  1.  
    1. Move the decimal point to create a number that is greater than or equal to 1 and less than 10.
      625097441 → ­­­­­­­­­­­______________________
    2. Count the number of times you moved the decimal point.
      625097441 → ­­­­­­­­­­­(fill in)____________________
    3. The decimal point was moved (fill in) ________ times to the left
    4. Use that value to determine the exponent. 
    5. Did you make the original number larger or smaller?
    6. This means the exponent will be positive or negative?
    7. What will the exponent value be? ____________
    8. Write the number in scientific notation:
      (fill in) ___________X________________
  1.  
    1. Move the decimal point to create a number that is greater than or equal to 1 and less than 10.
      0.0000717 → ____________
    2. Count the number of times you moved the decimal point.
      0.0000717 →  ­­­­­­­­­­­(fill in)____________________
    3. The decimal point was moved (fill in) ________ times to the right
    4. Use that number to determine the exponent. 
    5. Did you make the original number larger or smaller?
    6. This means the exponent will be positive or negative? 
    7. What will the exponent value be? ____________
    8. Write the number in scientific notation:(fill in) ___________X________________

Practice Problems

  1. Express the following numbers in scientific notation.
    1. 0.00012
    2. 1000
    3. 0.01
    4. 12
    5. 0.987
    6. 569
    7. 0.0000007
    8. 1,000,000
    9. 0.001257
    10. 987,653,000,000
    11. 11,020
    12. 0.000595

Challenge

The following scientific notation problems have errors. Identify the error and then correct the error.

Value
Identify Error and correctly write value
6.71 X 10⁷ = 671,000
27.8923 X 10⁸ = 278,923,000
5.17 X 10⁵ = 0.0000517