GRE - 1

1.7. Percent

The term percent means per hundred, or hundredths. Percents are ratios that are often used to represent parts of a whole, where the whole is considered as having 100 parts. Percents can be converted to fraction or decimal equivalents. Here are three examples of percents. Example 1.7.1: 1 percent means 1 part out of 100 […]

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1.6. Ratio

The ratio of one quantity to another is a way to express their relative sizes, often in the form of a fraction, where the first quantity is the numerator and the second quantity is the denominator. Thus, if s and t are positive quantities, then the ratio of s to t can be written as […]

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1.5. Real numbers

The set of real numbers consists of all rational numbers and all irrational numbers. The real numbers include all integers, fractions, and decimals. The set of real numbers can be represented by a number line called the real number line. Arithmetic Figure 2 below is a number line. Every real number corresponds to a point […]

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1.4. Decimals

The decimal number system is based on representing numbers using powers of 10. The place value of each digit corresponds to a power of 10. For example, the digits of the number 7,532.418 have the following place values. Arithmetic Figure 1 That is, the number 7,532.418 can be written as Alternatively, it can be written […]

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1.3. Exponents and roots

Exponents Exponents are used to denote the repeated multiplication of a number by itself; for example, 34=(3)(3) (3)(3)=81 and 35=(5) (5) (5)=125. In the expression 34, 3 is called the base, 4 is called the exponent, and we read the expression as “3 to the fourth power.” Similarly, 5 to the third power is 125. When the […]

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1.2. Fractions

A fraction is a number of the form , where c and d are integers and d ≠ 0. The integer c is called the numerator of the fraction, and d is called the denominator. For example, is a fraction in which -7 is the numerator and 5 is the denominator. Such numbers are also called rational numbers. Note that every integer n is a rational number, because n is equal to the […]

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1.1. Integers

The integers are the numbers 1,  2, 3, … , together with their negatives,-1,-2,-3, … , and 0. Thus, the set of integers is {. . . ,-3,-2,-1, 0, 1, 2, 3, . . .}. The positive integers are greater than 0, the negative integers are less than 0, and 0 is neither positive nor […]

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