Students attend to precision when adding numbers in scientific notation, taking care that the numbers are first written as a decimal or with powers of 10 with the same exponent (MP6). Students critique the reasoning of Diego, Clare, and Kiran as they make sense of adding numbers in scientific notation (MP3).

The purpose of this discussion is to highlight common misconceptions when adding or subtracting numbers in scientific notation and to introduce students to two possible strategies. Begin by asking students to share which students they agreed with and why. Here are some questions for discussion:

• “How are Clare’s and Kiran's approaches alike?” (They both reached the same sum by attending to place value.) 
• “How are their approaches different?” (Kiran wrote the numbers as decimals and added them. Clare wrote the numbers with the same power of 10 and added them. Kiran’s method might not work very well if the numbers are very large or very small. The decimal form of those numbers would be unwieldy.) 
• “Why must the terms have the same power of 10 to be added?” (We can only add digits that are of the same place value. If the powers of 10 are different, the place values of the digits in the first factors of the two expressions would be different. For example, the 4 in means 4 ten-thousands and the 1 in means 1 hundred-thousand, so we cannot add 4.9 and 1.2.)
• “How might Clare have reasoned that can be written as ?” (Changing 1.2 into 12 requires multiplying by 10. To keep the value of the expression the same, we must divide it by 10, which decreases the exponent by 1, from to .)
• “If the diameter of Jupiter is , are Neptune and Saturn side-by-side wider than Jupiter?” (Yes, since a width of is greater than a width of .

In this activity, students add quantities written in scientific notation in order to answer questions in context. To add numbers in scientific notation, students must reason abstractly and quantitatively by aligning place value and then interpreting their results in the context of the situation(MP2).

The goal of this discussion is to highlight that values given in scientific notation can be added by carefully aligning the place values of all of the addends. Display the table from the Task Statement for all to see and consider discussing the following questions: 

• “Can we easily add the diameters of Mercury and Mars? Why?” (Yes, because both measurements are written with the same power of 10, so we can add the first factors together.)
• “What are some other planet diameters that we can add together without any additional steps?” (Venus and Earth because their diameters are both written with the same power of 10.)
   

In this optional activity, students work with positive and negative exponents simultaneously. This activity may be useful if students need more experience with negative exponents or additional practice adding quantities expressed using scientific notation.

The goal of this discussion is to highlight the difference between multiplying or dividing numbers in scientific notation and adding and subtracting numbers in scientific notation. Here are some questions for discussion:

• “When using scientific notation, what are some differences between the strategies for multiplying or dividing numbers and the strategies for adding and subtracting?” (When multiplying or dividing, the numbers don’t have to have the same power of 10 like they do when adding or subtracting.)
• “Which operation do you think is the easiest? Hardest?” (Answers vary.)