ASVAB Arithmetic Reasoning Practice Test 398188

Questions 5
Topics Defining Exponents, Multiplying & Dividing Fractions, PEMDAS, Ratios, Scientific Notation

Study Guide

Defining Exponents

An exponent (cbe) consists of coefficient (c) and a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).

Multiplying & Dividing Fractions

To multiply fractions, multiply the numerators together and then multiply the denominators together. To divide fractions, invert the second fraction (get the reciprocal) and multiply it by the first.

PEMDAS

Arithmetic operations must be performed in the following specific order:

  1. Parentheses
  2. Exponents
  3. Multiplication and Division (from L to R)
  4. Addition and Subtraction (from L to R)

The acronym PEMDAS can help remind you of the order.

Ratios

Ratios relate one quantity to another and are presented using a colon or as a fraction. For example, 2:3 or \({2 \over 3}\) would be the ratio of red to green marbles if a jar contained two red marbles for every three green marbles.

Scientific Notation

Scientific notation is a method of writing very small or very large numbers. The first part will be a number between one and ten (typically a decimal) and the second part will be a power of 10. For example, 98,760 in scientific notation is 9.876 x 104 with the 4 indicating the number of places the decimal point was moved to the left. A power of 10 with a negative exponent indicates that the decimal point was moved to the right. For example, 0.0123 in scientific notation is 1.23 x 10-2.