Scientific Notation on the ACT Math Test

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 a_sn_img1 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.

a_sn_img2

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 a_sn_img3seconds. In fact, the reaction actually lasted 100 times longer than they expected. How long did the reaction actually last, in seconds?

a_sn_img4

Let’s start by writing out a_sn_img5 Since we have a negative exponent, we know the decimal will move to the left. .00000034 = a_sn_img5

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 a_sn_img6.  We can express the solution as: a_sn_img7 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).

 

By the way, Magoosh can help you study for both the SAT and ACT exams. Click here to learn more!

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