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Approximating a number A rational number is a number that can be written as a fraction of integers. An irrational number is a real number that is not rational. Numbers such as e, T and v2 are irrationals. These numbers can be represented by non-terminating and non- repeating decimals. A 9-digit calculator gives that the value of v2 is 1.41421356. If you square this number using the same calculator, you will get 2. However, if you use a calculator that allows for more digits, you will get a different number: (1.41421356)? = 1.9999999932878736. So 2 is just an approximation. In other words, v2 is not equal to 1.41421356, but we can say that v2 is approximately 1.41421356. In fact, the latter calculator will give a value for v2 that has the same decimals from before plus a few more: 1.414213562373095. This number is closer to v2 than 1.41421356. The more decimals, the better the approximation. We use the symbol 2 to indicate that the numbers are very close to each other, but not equal: V2 - 1.414213562373095. Practice Give a value that is close to 77 but not equal to 7T.

Approximating a number A rational number is a number that can be written as a fraction of integers. An irrational number is a real number that is not rational. Numbers such as e, T and v2 are irrationals. These numbers can be represented by non-terminating and non- repeating decimals. A 9-digit calculator gives that the value of v2 is 1.41421356. If you square this number using the same calculator, you will get 2. However, if you use a calculator that allows for more digits, you will get a different number: (1.41421356)? = 1.9999999932878736. So 2 is just an approximation. In other words, v2 is not equal to 1.41421356, but we can say that v2 is approximately 1.41421356. In fact, the latter calculator will give a value for v2 that has the same decimals from before plus a few more: 1.414213562373095. This number is closer to v2 than 1.41421356. The more decimals, the better the approximation. We use the symbol 2 to indicate that the numbers are very close to each other, but not equal: V2 - 1.414213562373095. Practice Give a value that is close to 77 but not equal to 7T.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 91E
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Approximating a number A rational number is a number that can be written as a fraction of integers. An irrational number is a real number that is not rational. Numbers such as e, ↑ and V2 are irrationals. These numbers can be represented by non-terminating and non- repeating decimals. A 9-digit calculator gives that the value of v2 is 1.41421356. If you square this number using the same calculator, you will get 2. However, if you use a calculator that allows for more digits, you will get a different number: (1.41421356)? = 1.9999999932878736. So 2 is just an approximation. In other words, v2 is not equal to 1.41421356, but we can say that v2 is approximately 1.41421356. In fact, the latter calculator will give a value for v2 that has the same decimals from before plus a few more: 1.414213562373095. This number is closer to v2 than 1.41421356. The more decimals, the better the approximation. We use the symbol 2 to indicate that the numbers are very close to each other, but not equal: V2 - 1.414213562373095. Practice Give a value that is close to 77 but not equal to 7T.
Transcribed Image Text:Approximating a number A rational number is a number that can be written as a fraction of integers. An irrational number is a real number that is not rational. Numbers such as e, ↑ and V2 are irrationals. These numbers can be represented by non-terminating and non- repeating decimals. A 9-digit calculator gives that the value of v2 is 1.41421356. If you square this number using the same calculator, you will get 2. However, if you use a calculator that allows for more digits, you will get a different number: (1.41421356)? = 1.9999999932878736. So 2 is just an approximation. In other words, v2 is not equal to 1.41421356, but we can say that v2 is approximately 1.41421356. In fact, the latter calculator will give a value for v2 that has the same decimals from before plus a few more: 1.414213562373095. This number is closer to v2 than 1.41421356. The more decimals, the better the approximation. We use the symbol 2 to indicate that the numbers are very close to each other, but not equal: V2 - 1.414213562373095. Practice Give a value that is close to 77 but not equal to 7T.
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