Examples-of-non-terminating-decimal

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From Encyclopedia

Numbers, Rational Numbers, Rational

A number in the form of a ratio a /b, where a and b are integers , and b is not equal to 0, is called a rational number. The rational numbers are a subset of the real numbers, and every rational number can be expressed as a fraction or as a decimal form that either terminates or repeats. Conversely, every decimal expansion that either terminates or repeats represents a rational number. Rational numbers can be written in several different forms using equivalent fractions. For example, . There are an infinite number of ways to write 1, ¼ or by multiplying both the numerator and denominator by the same nonzero integer. Therefore, there are an infinite number of ways to write every rational number in terms of its equivalent fraction. The following example shows how to find the ratio of integers that represents a repeating decimal. One way to compare two rational numbers is to convert them into a decimal form. Dividing the numerator by the denominator results in the decimal equivalent. If the division has no remainder, then the decimal is called a terminating decimal. For example, ½ = 0.5, , and . Although some decimals do not terminate, they do repeat because at some point a digit, or group of digits, repeats in a regular fashion. Examples of repeating decimals are ⅓ = 0.333…,, and . A bar written over the digits or group of digits that repeat shows that the decimal is repeating: , and . Rational numbers satisfy the following properties. see also Integers; Numbers, Irrational; Numbers, Real; Numbers, Whole. Rafiq Ladhani Amdahl, Kenn, and Jim Loats. Algebra Unplugged. Broomfield, CO: Clearwater Publishing Co., 1995. Miller, Charles D., Vern E. Heeren, and E. John Hornsby, Jr. Mathematical Ideas, 9th ed. Boston: Addison-Wesley, 2001.


From Omilili

Can NOT divide two Bigdecimals

Java.lang.ArithmeticException: Non-terminatingdecimal expansion; no exact representable decimal result... out I finally managed to take off the VAT with rounded to 2 Decimal places. t = new BigDecimal with rounded to 2 Decimal places... Two minor points: 1. The use of the BigDecimal(double) constructor

Basic concepts,fundas

Rational nos. a .terminatingdecimal fractions:4.25 b .Non terminatingdecimal fractions. ... terminating periodic fractions:5.3333 6.Irrational nos. non terminating non periodic fractions=5.234567 hi puys, i have seen threads similar to this one on pg but all those threads have high level fundas... so im starting this...

I dont knw how to write the decimals as comon fractoins in simplest form?...

For non-terminating, repeating decimals: 1. 0. ... Let x = 3. ... then 10x = 3. ... 10x - x = 3.333... .. - 0.3333... 9x = 3 (All of the 3's to the right of the decimal place cancel out) x = 3/9 = 1/3 ... decimals: 1. 0.465 Look at a non-zero digit which is in the smallest place. In this case it is the 5

From Yahoo Answers

Question:Ok, please not only answer these problems for me, but tell me what the words mean so that I know for future reference. Directions: Copy and complete the statement using always, sometimes, or never. 1. An integer is ______ a rational number. 2. A fraction can _______ be written as a terminating decimal 3. A repeating decimal is ________ a rational number. Thank you! (p.s. since you read this whole thing you get to know that the best answer gets ten points!)

Answers:1. An integer is ALWAYS a rational number. 2. A fraction can SOMETIMES be written as a terminating decimal. 3. A repeating decimal is ALWAYS a rational number. Integer = whole number which can be postive or negative Rational number = a number that can be expressed as a ratio of two integers Terminal decimal = a decimal that comes to an end at some point, e.g. 0.25, 0.145346, 0.123456789, or doesn't go on forever. Repeating decimal = a decimal that goes on forever, but the numbers repeat themselves, e.g. 0.333333..., 0.123412341234... and so on. The last one might be clearer with an example. A rational number by definition can be written in the form a/b, where both a and b are whole numbers, i.e. integers. So, for example, prove 0.16666.. is a rational number. Let's call 0.16666... x 100x = 16.666... 100x - x = 99x = 16.5 990x = 165 x = 165/990 = 33/198 Both 33 and 198 are rational, and if you stick that into a calculator it'll give you 0.1666..., proving the rule. Hope this makes sense.

Question:if an irrational number is a non repeating number, then why is 0.75 a rational number? Also what is the difference between a rational number and an irrational number?

Answers:When talking about rational and irrational numbers in decimal form, irrational numbers are numbers where the portion that comes after the decimal neither terminates (ends) nor repeats. Rational numbers in decimal form either terminate or repeat. Another way to think of this is by noticing that the two words that we are talking about both contain the root word "ratio". Ratios are often expressed in fractional form. An irrational number is not able to be placed into fractional form a rational number is able to be expressed as a fraction. 0.75 (the example that you used) is express-able as a fraction: 3/4. Numbers like Pi, and e are not rational, and cannot be expressed as fractions (that's why we gave them letters). They can be approximated by fractions, but have no true fractional form. (other irrational numbers are 'square root of 2', 'square root of 3"., and the famous "Golden Proportion". Many textbooks define rational numbers to be "any real number that can be expressed by a ratio of integers". A similar definition of irrational found in many texts would be: "any real number that is not rational" Or " any real number that can be written as a decimal but not as a fraction."

Question:for example, can -5 be considered a rational number?

Answers:A rational number is any number that can be written as a fraction. -5 is a rational number because you can write it -(5 over 1) An irrational number is a non-repeating, non-terminating (doesn't end) decimal, like pi. A repeating decimal can always be written over 9, like .4 repeating can be 4/9, and .423 repeating can be 423/999


From Youtube

Rational vs Irrational Numbers - YourTeacher.com - Math Help

For a complete lesson on rational vs irrational numbers, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn that the following number sets represent rational numbers natural numbers, whole numbers, integers, fractions, terminating decimals, and repeating decimals. For example, -2, 7, 3/4, 0.0006, and 0.191919... are all rational numbers. However, a decimal that is both non-terminating and non-repeating is an irrational number. For example, 0.12579835781... and 39.779778776775... are irrational numbers.


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