Class 8: Factors and Multiples (Lecture Notes)
... Class 8: Factors and Multiples (Lecture Notes) If a number ‘a’ divides another number ‘b’ exactly, then we say that ‘a’ is a factor of ‘b’ and ‘b’ is a multiple of ‘a’. Factor: A factor of a number is an exact divisor of that number. Multiple: A number is said to be a multiple of any of its factors. ...
... Class 8: Factors and Multiples (Lecture Notes) If a number ‘a’ divides another number ‘b’ exactly, then we say that ‘a’ is a factor of ‘b’ and ‘b’ is a multiple of ‘a’. Factor: A factor of a number is an exact divisor of that number. Multiple: A number is said to be a multiple of any of its factors. ...
What every computer scientist should know about floating
... if the real number .0314159 is represented as 3.14 x 10-2, then it is in error by .159 units in the last place. In general, if the floating-point number d. d . . . d x fle is used to represent z, it is in error by Id. d . . . d– ( z//3’) I flp - 1 units in the last place.4 The term ulps will be used ...
... if the real number .0314159 is represented as 3.14 x 10-2, then it is in error by .159 units in the last place. In general, if the floating-point number d. d . . . d x fle is used to represent z, it is in error by Id. d . . . d– ( z//3’) I flp - 1 units in the last place.4 The term ulps will be used ...
Integers - EduGAINS
... using number lines, sign is represented by direction, and size is represented by length (or distance). After the representations in different models are understood, contextual problems provide opportunities for students to develop conceptual understanding of operations with integers. When using colo ...
... using number lines, sign is represented by direction, and size is represented by length (or distance). After the representations in different models are understood, contextual problems provide opportunities for students to develop conceptual understanding of operations with integers. When using colo ...
Lecture #13 - February 27, 2004 - Introduction to Floating Point
... both a normalized fraction and a scale factor to properly position the binary point. In our earlier example we saw that the decimal number 23.375 is 10111.011 in binary. The normalized scientific notation version of 23.375 is 2.3375×101, and the normalized binary version of 10111.011 is 1.0111011×24 ...
... both a normalized fraction and a scale factor to properly position the binary point. In our earlier example we saw that the decimal number 23.375 is 10111.011 in binary. The normalized scientific notation version of 23.375 is 2.3375×101, and the normalized binary version of 10111.011 is 1.0111011×24 ...
Division by zero
In mathematics, division by zero is division where the divisor (denominator) is zero. Such a division can be formally expressed as a/0 where a is the dividend (numerator). In ordinary arithmetic, the expression has no meaning, as there is no number which, multiplied by 0, gives a (assuming a≠0), and so division by zero is undefined. Since any number multiplied by zero is zero, the expression 0/0 also has no defined value and is called an indeterminate form. Historically, one of the earliest recorded references to the mathematical impossibility of assigning a value to a/0 is contained in George Berkeley's criticism of infinitesimal calculus in The Analyst (""ghosts of departed quantities"").There are mathematical structures in which a/0 is defined for some a such as in Riemann spheres and real projective lines; however, such structures cannot satisfy every ordinary rule of arithmetic (the field axioms).In computing, a program error may result from an attempt to divide by zero. Depending on the programming environment and the type of number (e.g. floating point, integer) being divided by zero, it may generate positive or negative infinity by the IEEE 754 floating point standard, generate an exception, generate an error message, cause the program to terminate, or result in a special not-a-number value.