All integers are rational numbers how to#

Look at the decimal form of the fractions we just considered. We have also seen that every fraction is a rational number.

We can also change any integer to a decimal by adding a decimal point and a zero. We have seen that every integer is a rational number, since a = a 1 a = a 1 for any integer, a. Let's look at the decimal form of the numbers we know are rational. Write each as the ratio of two integers: ⓐ −19 −19 ⓑ 8.41. We can use the reciprocal (or multiplicative inverse) of the place value of the last digit as the denominator when writing the decimal as a fraction. In general, any decimal that ends after a number of digits (such as 7.3 7.3 or −1.2684 ) −1.2684 ) is a rational number. So 7.3 7.3 is the ratio of the integers 73 73 and 10. 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.

All integers are rational numbers how to#

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.