Scientific Notation is not a heavily-tested concept on the ACT. However, it may be combined with other topics for medium and hard-level questions. Use this guide to bolster your online studies and gain confidence for test day!
Large numbers and very small decimals are often expressed with exponents using scientific notation. Scientific notation involves writing the number as a product of a decimal and the number 10 raised to a certain power. The reason scientific notation is used is that is saves space. Who would want to write .000000000000000000547, when saves us a lot more room?
The value of the exponent indicates the number of places the decimal moves. In our example above, we moved the decimal 19 places to the right, so the exponent was a positive 19.
Golden Rules of Scientific Notation: Positive exponents move to the right. Negative exponents move to the decimal to the left. Try a practice question on your own!
Scientists testing a certain atomic reaction expected it to take place in seconds. In fact, the reaction actually lasted 100 times longer than they expected. How long did the reaction actually last, in seconds?
Let’s start by writing out Since we have a negative exponent, we know the decimal will move to the left. .00000034 =
Now we would multiply the decimal by 100. Since there are two zeroes in 100, the decimal will move two places to the right. The answer would be .000034. To rewrite that in Scientific Notation, we can move the decimal 5 places to the right again, which would be a negative exponent of 5. The answer is D.
A faster way to think about this question is to know that . We can express the solution as: If you remember your exponent rules, when we multiply exponents with the same base, we can add the exponents. -7 + 2 = -5. Again, this matches choice (D).