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Study Guide Review Study Guide Review
... 11. Sumaya is reading a book with 288 pages. She has already read 90 pages. She plans to read 20 more pages each day until she finishes the book. Determine how many days Sumaya will need to finish the book. In your answer, count part of a day as a full day. Show that your answer is reasonable. ...
... 11. Sumaya is reading a book with 288 pages. She has already read 90 pages. She plans to read 20 more pages each day until she finishes the book. Determine how many days Sumaya will need to finish the book. In your answer, count part of a day as a full day. Show that your answer is reasonable. ...
Classifying Real Numbers
... A rational number is a number that can be written as the ratio of two integers. An irrational number cannot be written as the ratio of two integers. • The square root of any whole number that is not a perfect square is irrational. The cube root of any integer that is not a perfect cube is irrational ...
... A rational number is a number that can be written as the ratio of two integers. An irrational number cannot be written as the ratio of two integers. • The square root of any whole number that is not a perfect square is irrational. The cube root of any integer that is not a perfect cube is irrational ...
P-adic number
In mathematics the p-adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a way different from the extension of the rational number system to the real and complex number systems. The extension is achieved by an alternative interpretation of the concept of ""closeness"" or absolute value. In particular, p-adic numbers have the interesting property that they are said to be close when their difference is divisible by a high power of p – the higher the power the closer they are. This property enables p-adic numbers to encode congruence information in a way that turns out to have powerful applications in number theory including, for example, in the famous proof of Fermat's Last Theorem by Andrew Wiles.p-adic numbers were first described by Kurt Hensel in 1897, though with hindsight some of Kummer's earlier work can be interpreted as implicitly using p-adic numbers. The p-adic numbers were motivated primarily by an attempt to bring the ideas and techniques of power series methods into number theory. Their influence now extends far beyond this. For example, the field of p-adic analysis essentially provides an alternative form of calculus.More formally, for a given prime p, the field Qp of p-adic numbers is a completion of the rational numbers. The field Qp is also given a topology derived from a metric, which is itself derived from the p-adic order, an alternative valuation on the rational numbers. This metric space is complete in the sense that every Cauchy sequence converges to a point in Qp. This is what allows the development of calculus on Qp, and it is the interaction of this analytic and algebraic structure which gives the p-adic number systems their power and utility.The p in p-adic is a variable and may be replaced with a prime (yielding, for instance, ""the 2-adic numbers"") or another placeholder variable (for expressions such as ""the ℓ-adic numbers""). The ""adic"" of ""p-adic"" comes from the ending found in words such as dyadic or triadic, and the p means a prime number.