Scientific Notation Operations
I can multiply and divide in scientific notation and adjust the answer so its coefficient is at least 1 and less than 10.
What students learn
Students learn to multiply and divide numbers in scientific notation, then adjust the coefficient and move the exponent the other way, so the value stays the same.
See inside
The key rule
When the coefficient is divided by 10, the exponent goes up by 1; when it is multiplied by 10, the exponent goes down by 1.
35 × 10⁶ = 3.5 × 10⁷; 0.6 × 10⁴ = 6 × 10³
Adjust until the coefficient is at least 1 and less than 10; the value never changes. To add, match the exponents first.
Watch out
A student adjusts 30 × 10⁻⁵ and writes 3 × 10⁻⁶.
The mistake: 30 × 10⁻⁵ = 3 × 10⁻⁶Both parts got smaller: the value is now 100 times too small.
The fix: 30 × 10⁻⁵ = 3 × 10⁻⁴30 went down to 3, so the exponent goes up: −5 + 1 = −4.
The mistakes it targets
- Moves the coefficient and the exponent the same way
- Leaves a coefficient of 10 or more unadjusted
- Subtracts a negative exponent as if it were positive
- Squares only the power of 10
- Adds before matching the exponents
The interactive Teacher Deck (32 slides, PowerPoint)
- The Learn page taught on screen: 8 fill-in blanks, each filled on its own click as students write it
- The worked example one slide per step (four steps), each with the reason for the step
- Six practice and three apply problems: a your-turn slide with a think-time bar, then the solution one line per click
- Jump buttons on every slide: go straight to any problem, the answer bank or the exit ticket
- Speaker notes on each problem: the question to ask, the worked answer and the common error to listen for
- A completed deck PDF (19 pages) with every slide fully built, to print or post
The student packet (9 pages)
- Learn: guided notes with four definitions, the key rule, a worked example and a Watch Out error pair
- Practice: two warm-up, two standard and two stretch problems, with an answer bank for self-checking that hides three common-mistake decoys
- Apply: one word problem, a reasoning prompt and one error analysis
- Assess: an exit ticket of four items, two per page, with an I-can self-rating
- Homework (page 5): eight new problems, two warm-up, four standard and two stretch
- Answer key (pages 6–7): every problem worked step by step, five common mistakes with what to do about each, and a grading guide, plus the homework key (page 8)
- Color and ink-saver editions of the whole packet
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.