Repeating decimals to rational numbers

• 4.4 Rational Numbers - Prince William County Public Schools

  long division to write fractions and mixed numbers as decimals. These decimals are also rational numbers and will either terminate or repeat. A terminating decimal is a decimal that ends. 1.5, 0.25, 10.625 A repeating decimal is a decimal that has a pattern that repeats. 1.333 . . . = 1. — 3 0.151515 . . . = 0. —15 Use bar notation to show

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• [PDF File]Rational Numbers & Periodic Decimal Expansions rational number 1 2 3 ...

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  rational numbers and the numbers with periodic or finite decimal expansions. That is, numbers such as 1 3 have the unending, but repeating, decimal expansion .333 … . Often to provide a precise but succinct way to write such decimal expansions, the repeating part is written only once and marked with an overbar. For instance, 1 3 = . _ 3 and 3 ...

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• [PDF File]Repeating and Terminating Decimals single spaced - CIESE

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  Lesson on Repeating and Terminating Decimals Dana T. Johnson 6/03 College of William and Mary dtjohn@wm.edu Background: This lesson would be embedded in a unit on the real number system. The set of real numbers can be thought of as the union of two sets of numbers, the rational numbers

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• [PDF File]Chapter 3 Lesson 1 Rational Numbers - WPMU DEV

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  1 Rational Numbers Repeating Decimals Notes 2017­2018.notebook September 13, 2017 Rational numbers Integers whole numbers natural numbers Write each fraction or mixed number as a decimal. 1) 5 8 = 2) ­12 3 Got it? You try... 4. ­2 3. 3 9 4 Write 0.45 as a fraction. Be sure to simplify completely.

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• [PDF File]CHAPTER 3 RATIONAL NUMBERSName: - Commack Schools

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  3­1a Terminating and Repeating Decimals.notebook. Note: When you see a fraction with the denominator of 9, remember that it represents a repeating decimal. To change a fraction into a decimal, divide the denominator into the numerator. To change a decimal into a percent, multiply the decimal by 100.

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• [PDF File]Decimal expression of rational numbers with repeating zeros

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  n be a rational number in lowest terms. Prove that is has a decimal expression ending in repeating zeros (0000:::) iff n=2a5b, for a;b 2Z, where a;b >0. Proof. We have to prove an if-and-only-if statement, so we need to go in both directions. ()): Let m n have a decimal expression ending in repeating zeros, that is m n = a0:a1:::a k00000 ...

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• [PDF File]Name: Chapter 2 Rational Numbers - Commack Schools

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  3­1b CN Terminating and Repeating Decimals.notebook 4 Sometimes you will get a: Repeating decimal: Reminder: use the bar notation to illustrate a repeating decimal * Example 1 Example 2 Example 3 Notice the repeating bar is over both the 2 and the 7 because both numbers consistently repeat.

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• [PDF File]Rational Numbers, Decimals, Geometric Series, Approximations

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  3. Find the decimal representation for the following numbers. If you obtain a repeating decimal, be sure to clearly show which digits repeat. 1 8 2 3 5 6 3 16 4 9 3 80 3 7 4. The repeating decimal 0.45981 = 0.459818181... has a period of length 2 since 81 repeats. One might be tempted to say that the period could also be 4 since 8181 repeats ...

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• [PDF File]Terminating and Repeating Decimals

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  Terminating and Repeating Decimals Student Probe Write 5 8 as a decimal. Answer: 0.625 Lesson Description In this lesson students use long division to convert fractions into repeating or terminating decimals. Calculator use in encouraged. Rationale All rational numbers, including mixed numbers, can be converted into repeating or terminating ...

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• [PDF File]Converting Repeating Decimals to Rational Numbers - Weebly

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  numbers, we said Irrational numbers are decimals that literally continue forever, and that they never form a pattern nor do they converge to a repeating number such as . The purpose of this lesson is to learn how to convert any repeating decimal, whether a repeating single digit or a repeating series, into a rational number or a fraction. Consider

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• [PDF File]7.4 Repeating DecimalsR - Big Ideas Learning

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  Extension Repeating DecimalsR 7.4 Rational Numbers In this extension, you will w rite a repeating decimal as a fraction. Writing a Repeating Decimal as a Fraction Let a variable x equal the repeating decimal d. Step 1: Write the equation x = d. Step 2: Multiply each side of the equation by 10n to form a new equation, where n is the number of ...

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• Repeating decimals - JSTOR Home

  Relatively few rational numbers are expressible as terminating decimals. On the other hand, all rational numbers can be expressed as repeating decimals. The nota-tion of repeating decimals is commonly introduced to the child but algorithms for operations with this notation are ignored. A positive rational number is the ratio

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• [PDF File]Rational Numbers: Decimals

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  rational numbers: 12 3 (or 31) 2.15 (or 215100) –0.37 (or –37100) 20% (or 0.2 or 210) Terminating and Repeating Decimals When you use long division to divide one integer by a nonzero integer, one of two interesting things can happen. The number may be represented by a terminating decimal, or the number may be represented by a repeating decimal.

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• [PDF File]14.4 Repeating Decimals - Big Ideas Learning

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  Extension Repeating Decimals 14.4 Rational Numbers In this extension, you will w rite a repeating decimal as a fraction. Writing a Repeating Decimal as a Fraction Let a variable x equal the repeating decimal d. Step 1: Write the equation x = d. Step 2: Multiply each side of the equation by 10n to form a new equation, where n is the number of ...

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• [PDF File]CONVERTING REPEATING DECIMALS TO FRACTIONS LESSON 3-D

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  Lesson 3-D ~ Converting Repeating Decimals To Fractions 17 A number that can be expressed as a fraction of two integers is called a rational number. Every rational number can be written as a decimal number. The decimal numbers will either terminate (end) or repeat. Terminating Decimals Repeating Decimals 3 4 = 0.75 19 10 = 1.9 394

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• [PDF File]REPEATING DECIMALS AND IRRATIONAL NUMBERS ON THE NUMBER INE THROUGH THE ...

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  Key words: Repeating Decimals, Irrational Numbers, Number Line, Pre-service Teachers, In-service Teachers 1. Introduction The set of real numbers include both the sets of rational numbers and irrational numbers. Rational numbers can be defined as a ratio of two integers whereas irrational numbers are numbers that cannot

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• Repeating Decimals and Fractions T NOTES - Texas Instruments

  Teacher Tip: You might need to remind your students that all rational numbers can be expressed as fractions or decimals with a finite number of digits or infinitely repeating digits. Numbers like 2.34 and 0.265 are rational and are sometimes called terminating decimals because the number of digits after the decimal point is finite.

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• [PDF File]Repeating Decimals - Kevin Carmody

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  This document derives several theorems on terminating and repeating decimals, along with illustrative examples. It is shown that every rational num-ber has a unique decimal representation, except that some rational numbers have two representations, such as 0:999:::=1. It is also shown which rational numbers result in terminating, pure re-

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