ACT Math

SAT Question of the Day

The SAT question of the day is a Functions Question that has already been addressed on this blog: click here to see an explanation.

ACT Math Question of the Day

This math question tests your knowledge of the distance formula and scientific notation.

A particle travels 1 × 10^8 centimeters per second in a straight line for 4 × 10^–6seconds. How many centimeters has it traveled?

This question asks you to find a distance.  The distance formula is rate × time = distance.  Plug in your rate (cm/sec) and your time (sec):

(1 × 10^8)(4 × 10^–6) = distance

At this point you could try to count zeros or plug this into your calculator.  It is actually faster if you just think about the properties of multiplication.  Remember that it doesn’t matter which order you use when multiplying several numbers together.  If you want your answer to remain in scientific notation, multiply the single digit numbers by each other and the tens by each other.  You know that 1 × 4 = 4.  You also know that 10^8 × 10^–6 = 10^2.  Therefore, you answer is 4 × 10^2.

Note: Working with exponents is not difficult!  Remember that if you are multiplying two base numbers that are the same (your 10s), all you need to do is add the exponents to find the power of your answer.  8 + (-6) = 2.  This works because raising a number to a negative power is really the same thing as putting it on the bottom of a fraction that many times.  Another way to think about 10^8 × 10^–6 = 10^2 is to imagine eight 10s on the top of a fraction and six 10s on the bottom.  After you cancel as many 10s as you can, there are still two 10s on top, which is your 10^2.

F. 2.5 × 10^2

G. 2.5 × 10^13

H. 4 × 10^2

J. 4 × 10^–14

K. 4 × 10^–48

The correct answer is (H).

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