Decimal and Rational Numbers

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• Convergent Sequence of Rationals

  Then a_n is rational for every n >= 1, since (a) both y and 1/n are rational and (b) the difference of two rational numbers is rational. Clearly, the sequence {a_n} converges to y. Example: y = 3.

• Rational vs. irrational

  pi is an irrational number because it is a non-recurrent, never ending decimal number. Non-terminating recurrent decimal numbers are rational numbers, because they can be reduced to the standard form of rational numbers.

• Members of the Given Real Number Subset

  In another word, rational numbers are 17, -12, 0, 7/8, 2 = square root of 4, 0.2 as a repeating decimal, 0.007 5.

• Rational Expressions vs. Rational Numbers

  A rational number is a number that can be expressed as a fraction, ratio of two integers or decimal number. Rational numbers can be ordered in a number line.

• How is doing operations (adding, multiplying, and dividing) with rational expressions similar to or different from doing operations with fractions?

  A rational number is a number that can be expressed as a fraction,ratio of two integers or decimal number. Rational numbers can be ordered in a number line.

• A Set Theory in Real Analysis

  230556 A Set Theory in Real Analysis Formal Math Proofs Prove that each of the following sets is countable: a) The set of all numbers with two distinct decimal expansions (like 0.500... and 0.4999...); b) The set of all rational points in the

• apply a factoring formula

  Is "548/799" a rational or irrational number? Explain. Fractions are rational numbers by definition. Simplify "(5 + 3i)(5 - 3i)." Is the result real, complex, or both? Explain.

• Algebra - Radicals - Practice Problems

  Give an exact answer and an approximation to three decimal places What is the exact value of c, what is the value of c approximated to three decimal places? 4. Multiply and simplify by factoring 5. Simplify 6.

• Intervals with rational endpoints as a basis for topology

  If both a and b are rational, there is nothing to prove. If a is irrational and b is rational, consider a sequence of rational numbers a_n, where a_n is the decimal representation of a kept up to the nth place after the decimal point.