Can we write it as a ratio of two integers? Because 7.3 7.3 means 7 3 10, 7 3 10, we can write it as an improper fraction, 73 10. The integer −8 −8 could be written as the decimal −8.0. We've already seen that integers are rational numbers. What about decimals? Are they rational? Let's look at a few to see if we can write each of them as the ratio of two integers. Remember that all the counting numbers and all the whole numbers are also integers, and so they, too, are rational. Since any integer can be written as the ratio of two integers, all integers are rational numbers. An easy way to do this is to write it as a fraction with denominator one.ģ = 3 1 −8 = −8 1 0 = 0 1 3 = 3 1 −8 = −8 1 0 = 0 1 We will now look at the counting numbers, whole numbers, integers, and decimals to make sure they are rational.Īre integers rational numbers? To decide if an integer is a rational number, we try to write it as a ratio of two integers. The definition of rational numbers tells us that all fractions are rational. We need to look at all the numbers we have used so far and verify that they are rational. A few examples areĤ 5, − 7 8, 13 4, and − 20 3 4 5, − 7 8, 13 4, and − 20 3Įach numerator and each denominator is an integer. Īll fractions, both positive and negative, are rational numbers. Do you remember what the difference is among these types of numbers?Ī rational number is a number that can be written in the form p q, p q, where p p and q q are integers and q ≠ o. We have already described numbers as counting numbers, whole numbers, and integers. And we'll practice using them in ways that we'll use when we solve equations and complete other procedures in algebra. We'll work with properties of numbers that will help you improve your number sense. We'll take another look at the kinds of numbers we have worked with in all previous chapters. In this chapter, we'll make sure your skills are firmly set. You have established a good solid foundation that you need so you can be successful in algebra. You have solved many different types of applications. You have become familiar with the language and symbols of algebra, and have simplified and evaluated algebraic expressions. You have learned how to add, subtract, multiply, and divide whole numbers, fractions, integers, and decimals. Identify Rational Numbers and Irrational NumbersĬongratulations! You have completed the first six chapters of this book! It's time to take stock of what you have done so far in this course and think about what is ahead. The correct answer is rational and real numbers.\) The number is between integers, so it can't be an integer or a whole number. ![]() ![]() The correct answer is rational and real numbers. The number is between integers, not an integer itself. ![]() All rational numbers are real numbers, so this number is rational and real. It's written as a ratio of two integers, so it's a rational number and not irrational. The correct answer is rational and real numbers, because all rational numbers are also real. Irrational numbers can't be written as a ratio of two integers. All rational numbers are also real numbers. The number is rational (it's written as a ratio of two integers) but it's also real. whole numbers, integers, rational numbers, and real numbers.integers, rational numbers, and real numbers.
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