Activity Sheet for the December, 2014, MATHCOUNTS Mini Try
... 1. To express 20 as a sum of different powers of 2, we would write 20 = 24 + 22 . The sum of the exponents of these powers is 4 + 2 = 6. If 400 were expressed as a sum of at least two distinct powers of 2, what would be the least possible sum of the exponents of these powers? 2. What is the base 4 r ...
... 1. To express 20 as a sum of different powers of 2, we would write 20 = 24 + 22 . The sum of the exponents of these powers is 4 + 2 = 6. If 400 were expressed as a sum of at least two distinct powers of 2, what would be the least possible sum of the exponents of these powers? 2. What is the base 4 r ...
Module 3 Topic A Lesson 1 ~ Homework
... Name ___________________________ Section 6 - _____ Date ____________ # ...
... Name ___________________________ Section 6 - _____ Date ____________ # ...
To evaluate integer questions that involve multiple signs:
... The addition of integers can be shown by moves on a number line. - Start at the first integer - Move to the right for positive integers - Move to the left for negative integers To subtract an integer, add its opposite. Example 1: Evaluate. a) (+3) + (+4) b) (-3) + (-4) c) (+3) + (-4) d) (-3) + (+4) ...
... The addition of integers can be shown by moves on a number line. - Start at the first integer - Move to the right for positive integers - Move to the left for negative integers To subtract an integer, add its opposite. Example 1: Evaluate. a) (+3) + (+4) b) (-3) + (-4) c) (+3) + (-4) d) (-3) + (+4) ...
Name - Typepad
... Rational: Can be written as a fraction Irrational: Unsimplified Radical or Non repeating decimal ...
... Rational: Can be written as a fraction Irrational: Unsimplified Radical or Non repeating decimal ...
Rules for Computation of Integers
... Look at the type of numbers you are to add (positive or negative) If the signs are the same (both positive or both negative) add the absolute value of the numbers If the signs are different subtract the absolute values of the numbers The answer's sign (+ or -) is determined by the number with the la ...
... Look at the type of numbers you are to add (positive or negative) If the signs are the same (both positive or both negative) add the absolute value of the numbers If the signs are different subtract the absolute values of the numbers The answer's sign (+ or -) is determined by the number with the la ...
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.