Eighth Grade · Math · week 22

Operations in scientific notation

Multiply and divide numbers in scientific notation, adjusting the result back into proper form.

Multiplying in scientific notation: multiply the front numbers, and ADD the exponents (the product rule from three weeks ago). Dividing: divide the front numbers, and SUBTRACT the exponents. Either way, if the front-number result lands outside 1-to-10, shift the decimal and adjust the exponent by one to fix it.

Do the front-number arithmetic and the exponent arithmetic as two separate, clearly labeled steps -- mixing them into one sloppy line is where errors creep in.

📋 For the teacher
Teach it (10–15 min):
  • Multiplying and dividing in scientific notation reuse the exact exponent rules from two weeks ago -- point out that this is not new material.
  • After combining the front numbers, always check whether the result is still between 1 and 10 -- if it is 10 or more, shift the decimal left and raise the exponent; if it is less than 1, shift right and lower the exponent.
  • Keep the front-number arithmetic and the exponent arithmetic as two separate, clearly labeled mini-steps.
  • This week only covers multiply and divide; adding and subtracting needs matching exponents first, which is worth a quick mention but is far less common in real use.
Talk about it:
  • Why do you add exponents when multiplying but subtract them when dividing?
  • What tells you a front-number result needs to be adjusted?
  • If you shift the decimal LEFT in the front number, why does the exponent go UP?

Mastery looks like: They multiply and divide numbers in scientific notation, correctly adjusting any front number that lands outside the 1-to-10 range.

Common stumbles: Forgetting to adjust when the front-number product is 10 or more; adjusting the exponent in the wrong direction when fixing an out-of-range front number.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

MultiplicationEqual groups and arrays make products finally click.try →DivisionShare fairly and build equal groups.try →
Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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