Answer to Question #114301 in Algebra for Felicia Ngubandze

Question #114301
1. Express 54069,269 in words; place value; and in terms of the powers of 10.
2. Differentiate between real and non-real numbers (give an examples).
1
Expert's answer
2020-05-13T19:05:18-0400
  1. Fifty-four million sixty-nine thousand two hundred sixty-nine.

Place value: 54069,269 = (5 x 10000000) + (4 x 1000000) + (6 x 10000) + (9 x 1000) + (2 x 100) + (6 x 10) + (9 x 1) = 50000000 + 4000000 + 60000 + 9000 + 200 + 60 + 9

5 - ten million's place

4 - million's place

6 - ten thousand's place

9 - thousand's place

2 - hunderd's place

6 - ten's place

9 - one's place

54069,269 = 0.54069269 x 108 = 54.069269 x 106 = 54069.269 x 103 = 54069,269 x 100 =

= 5406926,900 x 10-2 = 54069269000,000 x 10-6


2. Main differences between complex and real numbers:

  • complex numbers cannot be compared (< or >)
  • every polynomial with real or complex coefficients has so many complex roots what is its degree
  • in a system of real numbers, a root of even degree cannot be extracted from a negative number. For complex numbers, it is possible to extract the root from any number of any degree, however, the result is ambiguous - the complex root of the nth degree from a nonzero number has n different complex values

Examples: you can compare real numbers, for instance, -120 < 5.67 or "\\dfrac{1}{3}" > "\\dfrac{2}{27}" , but you can't do this to complex numbers. Polynomial x4 + 2x3 + x2 + 5x +12 would have 4 roots(with complex roots), because n = 4. Also for equation like x2 = -1 there will be two solutions: i and -i.


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