Operations with Scientific Notations

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SWBAT understand and use scientific notation to compute products, quotients, and compare amounts.

Big Idea

Comparing large or small numbers is almost always easier using scientific notation.


10 minutes

Pair students up asking one in each pair to handle the calculator. Hand each pair a SCINOTE ENTRANCE CARD.docx card. 

In Part 1:

Ask the students to evaluate the 3 expressions on the card and then write a rule that could be used to multiply two numbers in scientific notation. Give students a few minutes to finish this task. Ask that the rule be written on the card and they not go onto part 2.  

Allow enough time for  everyone to get a shot at writing a rule, then call on someone to share their rule. Accept any answer but single out the rule that takes the product of the decimal and that of the powers, separately. Ask students if this looks easier and if it works. Ask them to go on to part 2. 

In Part 2

Ask students to evaluate these expressions and state if their rule works for these expressions as well.  Tell students to explain why or why not their rule applies. You will want to make sure that students understand that the rule applies but the answer must be adjusted to be in proper scientific notation.


10 minutes

After completion of the Launch Activity ask students, "What property of real numbers is being exhibited in the rule that we wrote describing how to perform the multiplication?"

It is my experience that students may say the popular Distributive Property. Once the correct property is determined (Associative Property of Multiplication), it would be a good moment to ask why the Distributive Property is NOT being used in this situation. I find that it is helpful to remind students that the Distributive Property of Multiplication distributes multiplication over addition or subtraction. Therefore, it does not apply to expressions like the ones in the Launch Activity. Complete the discussion by ask students to provide a clear explanation why the Associative Property allows the operations to be performed on these expressions. 

Refer students back to the Launch problem in the previous lesson where they had to compare the surface areas of Jupiter and Earth. They found that Jupiter's surface area was nearly 120 times larger than Earth's. Ask if they recall how they found this ratio.

As you listen to the student explanations, write both surface areas on the board and ask them to use the rule they just came up with to see if it works: 

 JUPITER:  6.1544 x 1010

 EARTH:  5.144576 x 108

Students will discover that it does, though the associative property won't be as clear to them here. Write the quotient on the board and show where the associative property is applied:

6.1544 x 1010 /5.144576 x 108

(6.1544/5.144576) x (1010/108) 



25 minutes

The problems on this NOTATION EXERCISE SHEET.docx involve using scientific notation. Students may use a calculator, but the work of calculating the results should be shown.

Common mistakes to be on the watch for:

Q1: Watch for students dividing both the decimal coefficient and the power by 3. Tell these students that dividing by 3 is like dividing by 3 x 100 

Q3: Watch for those students who love the Distributive Property so much that they apply it when it does not apply. 

Q5: Students sometimes forget the rules for subtracting integers when dividing negative powers. Be prepared to remind them. For this problem, students may end up with 10-11 instead of 10-3



5 minutes
To close the lesson, ask students to reflect on what they've learned in today's lesson and previous lessons on scientific notation. The back of their Notation Exercise Sheet can be used to answer the following 3 questions. Student reflections are useful because help you to determine if additional practice is needed, if you need to reteach something, or you can move on to the next lesson.
Ask students to answer
  •  I really understood this……
  • Before I can say I understand, I have a few questions about… 
  •  I don’t even know where to start on …



This website can be used to practice scientific notation before doing the homework assignment. Multiplying, dividing, and conversions can be practiced.