©Artist_R/Shutterstock.com- Integer: An integer is any positive or negative whole number or zero. The ASVAB often requires you to work with integers, such as –6, 0, or 27.
- Numerical factors: Factors are integers (whole numbers) that can be divided evenly into another integer. To factor a number, you simply determine the numbers that you can divide into it. For example, 8 can be divided by the numbers 2 and 4 (in addition to 1 and 8), so 2 and 4 are factors of 8. The prime factorization of the number 30 is written 2 × 3 × 5.
Numbers may be either composite or prime, depending on how many factors they have:
- Composite number: A composite number is a whole number that can be divided evenly by itself and by 1, as well as by one or more other whole numbers; in other words, it has more than two factors. Examples of composite numbers are 6 (whose factors are 1, 2, 3, and 6), 9 (whose factors are 1, 3, and 9), and 12 (whose factors are 1, 2, 3, 4, 6, and 12).
- Prime number: A prime number is a whole number that can be divided evenly by itself and by 1 but not by any other number, which means that it has exactly two factors. The number 1 is not a prime number. Examples of prime numbers are 2 (whose factors are 1 and 2), 5 (whose factors are 1 and 5), and 11 (whose factors are 1 and 11).
- Base: A base is a number that’s used as a factor a specific number of times — it’s a number raised to an exponent. For instance, the term 43 (which can be written 4 × 4 × 4, and in which 4 is a factor three times) has a base of 4.
- Exponent: An exponent is a shorthand method of indicating repeated multiplication. For example, 15 × 15 also can be expressed as 152, which is also known as “15 squared” or “15 to the second power.” The small number written slightly above and to the right of a number is the exponent, and it indicates the number of times you multiply the base by itself. Note that 152 (15 × 15), which equals 225, isn’t the same as 15 × 2 (which equals 30).
To express 15 × 15 × 15 using this shorthand method, simply write it as 153, which is also called “15 cubed” or “15 to the third power.” Again, 153 (which equals 3,375) isn’t the same as 15 × 3 (which equals 45).
- Square root: The square root of a number is the number that, when multiplied by itself (in other words, squared), equals the original number. For example, the square root of 36 is 6. If you square 6, or multiply it by itself, you produce 36.
- Factorial: A factorial is an operation represented by an exclamation point (!). You calculate a factorial by finding the product of (multiplying) a whole number and all the whole numbers less than it down to 1. That means 6 factorial (6!) is 6 × 5 × 4 × 3 × 2 × 1 = 720.
A factorial helps you determine permutations — all the different possible ways an event may turn out. For example, if you want to know how many different ways six runners could finish a race (permutation), you would solve for 6!: 6 × 5 × 4 × 3 × 2 × 1.
- Reciprocal: A reciprocal is the number by which another number can be multiplied to produce 1; if you have a fraction, its reciprocal is that fraction turned upside down. For example, the reciprocal of 3 is 1/3. If you multiply 3 times1/3, you get 1. The reciprocal of 1/6 is 6/1 (which is the same thing as 6)
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The reciprocal of 2/3 is 3/2. The number 0 doesn’t have a reciprocal. Get the idea?
- Rounding: Rounding is limiting a number to a certain number of significant digits (replacing some digits with zeroes). You perform rounding operations all the time — often without even thinking about it. If you have $1.97 in change in your pocket, you may say, “I have about two dollars.” The rounding process simplifies mathematical operations.
Often, numbers are rounded to the nearest tenth. The ASVAB may ask you to do this. If the number you’re eliminating is 5 or over, round up; for any number under 5, round down. For example, 1.55 rounded to the nearest tenth can be rounded up to 1.6, and 1.34 can be rounded down to 1.3.
Many math problems require rounding—especially when you’re doing all this without a calculator. For example, pi (π) represents a number approximately equal to 3.141592653589793238462643383 (and on and on and on). However, in mathematical operations and on the ASVAB, it’s common to round π to 3.14.