1 REAL NUMBERS CHAPTER
... Clearly, the denominator is not of the form 2m × 5n. Hence, it has non-terminating repeating decimal expansion. Example 10. The following real numbers have decimal expression as given below. In each case decide whether ...
... Clearly, the denominator is not of the form 2m × 5n. Hence, it has non-terminating repeating decimal expansion. Example 10. The following real numbers have decimal expression as given below. In each case decide whether ...
101215 Scientific Notation v2
... Scientific Notation is used to express very large and very small numbers so that problem solving will be easier. ...
... Scientific Notation is used to express very large and very small numbers so that problem solving will be easier. ...
Full text
... which to date has not been determined in a precise manner. In the face of this situations what remains to be done? The present a r t i cle attacks this problem by attempting to accomplish two things.9 (1) Determining the relations among cognate formulas so that formulas can be grouped into families ...
... which to date has not been determined in a precise manner. In the face of this situations what remains to be done? The present a r t i cle attacks this problem by attempting to accomplish two things.9 (1) Determining the relations among cognate formulas so that formulas can be grouped into families ...
1/4 -1/4
... Change mixed numbers to improper fractions before multiplying Example: 1 5/8n = 25 13/8n = 25 (8/13)(13/8)n = 25(8/13) n = 15 5/13 ...
... Change mixed numbers to improper fractions before multiplying Example: 1 5/8n = 25 13/8n = 25 (8/13)(13/8)n = 25(8/13) n = 15 5/13 ...
Arithmetics on number systems with irrational bases
... β-expansion of x + y, x − y, and x × y with the knowledge of the β-expansions of x ...
... β-expansion of x + y, x − y, and x × y with the knowledge of the β-expansions of x ...
Multiplication of a Fraction by a Fraction
... Interpret the product of (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/ ...
... Interpret the product of (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/ ...
CompOrgW3LArith Floa..
... Fractions: Multiply or Divide, then normalise use 3-bit fractions in the following: eg Multiply 0.101 x 2^2 by –0.110 x 2 ^-3 Operand Signs differ, so result will have -ve sign. Add exponents for multiplication: 2+ (-3) = -1 is the result exponent. Multiply fractions: 0.101 x 0.110 gives 0.01111 If ...
... Fractions: Multiply or Divide, then normalise use 3-bit fractions in the following: eg Multiply 0.101 x 2^2 by –0.110 x 2 ^-3 Operand Signs differ, so result will have -ve sign. Add exponents for multiplication: 2+ (-3) = -1 is the result exponent. Multiply fractions: 0.101 x 0.110 gives 0.01111 If ...
ORAL QUESTIONS CLASS VII : INTEGERS
... 14. A median connects a vertex to the mid. point of the opposite side in a triangle 15. An altitude has one end point at a vertex of a triangle and the other on the line containing the opposite side. 16. An exterior angle of a triangle = sum of its interior opposite angles. 17. The sum of three angl ...
... 14. A median connects a vertex to the mid. point of the opposite side in a triangle 15. An altitude has one end point at a vertex of a triangle and the other on the line containing the opposite side. 16. An exterior angle of a triangle = sum of its interior opposite angles. 17. The sum of three angl ...
Decimal expansions of fractions
... • The expansion of 1/p in any base B has a period of repetition dividing p − 1. One interesting, maybe unexpected, thing is that it doesn’t depend all that much on the base B. To begin, suppose 1/p has a period of repetition N . It is easy enough to see that it has a simple repeat, starting right at ...
... • The expansion of 1/p in any base B has a period of repetition dividing p − 1. One interesting, maybe unexpected, thing is that it doesn’t depend all that much on the base B. To begin, suppose 1/p has a period of repetition N . It is easy enough to see that it has a simple repeat, starting right at ...
Chapter 7
... Multiplication - define resultant field equal to sum of lengths of operands begin multiplied Division - define resultant field equal to sum of number of digits in divisor and dividend ...
... Multiplication - define resultant field equal to sum of lengths of operands begin multiplied Division - define resultant field equal to sum of number of digits in divisor and dividend ...
Approximations of π
Approximations for the mathematical constant pi (π) in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning of the Common Era (Archimedes). In Chinese mathematics, this was improved to approximations correct to what corresponds to about seven decimal digits by the 5th century.Further progress was made only from the 15th century (Jamshīd al-Kāshī), and early modern mathematicians reached an accuracy of 35 digits by the 18th century (Ludolph van Ceulen), and 126 digits by the 19th century (Jurij Vega), surpassing the accuracy required for any conceivable application outside of pure mathematics.The record of manual approximation of π is held by William Shanks, who calculated 527 digits correctly in the years preceding 1873. Since the mid 20th century, approximation of π has been the task of electronic digital computers; the current record (as of May 2015) is at 13.3 trillion digits, calculated in October 2014.