Scientific notation writes a number as a times 10 to the n, where 1 is less than or equal to the absolute value of a and a is less than 10, and n is an integer. Multiplying and dividing these forms is just exponent rules plus moving the decimal. The ACT uses it for big populations, tiny measurements, and quick arithmetic without a calculator.
Reading the form
3.2 times 10^4 means 3.2 with the decimal moved four places right: 32,000. 5.7 times 10^-3 means three places left: 0.0057. The exponent tells you how many places and which direction. Positive moves right, negative moves left.
Multiply and divide
Multiply the leading numbers, add the exponents. (2 times 10^3)(4 times 10^5) = 8 times 10^8. Divide the leading numbers, subtract exponents. (6 times 10^7) / (2 times 10^4) = 3 times 10^3. These are the same product and quotient rules from exponent rules on the ACT.
Adjust when a is out of range
After you combine, a must stay between 1 and 10. If you get 45 times 10^6, rewrite 45 as 4.5 times 10, so the answer is 4.5 times 10^7. If you get 0.32 times 10^5, rewrite 0.32 as 3.2 times 10^-1, so the answer is 3.2 times 10^4. One adjustment step fixes most wrong answers.
Adding and subtracting
Match the power of 10 first. You cannot add 3 times 10^4 and 5 times 10^3 directly—rewrite 5 times 10^3 as 0.5 times 10^4, then add to get 3.5 times 10^4. Same idea as combining like terms.
Calculator-free moves
When a question asks you to compare two numbers in scientific notation, compare exponents first. If those tie, compare the leading numbers. When it asks for ordinary form, move the decimal and count carefully— off-by-one on the exponent is the classic trap.
Where it shows up
Scientific notation sits inside Preparing for Higher Math and Integrating Essential Skills, often bundled with growth or scale word problems. For how it fits the rest of the section, see the full list of ACT Math topics. Drill the exponent rules until they are automatic, and these questions become quick points.
Start practicing
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This article offers general ACT prep guidance. The ACT can change from year to year, including its format, scoring, policies, test dates, and fees, so always confirm the latest details on the official ACT website at act.org before you make decisions. ACT® is a registered trademark of ACT, Inc. thirty-six is not affiliated with, endorsed by, or sponsored by ACT.