 1.7.1: A positive number is written in scientific notation when it is expr...
 1.7.2: True or false: 7 * 104 is written in scientific notation.
 1.7.3: True or false: 70 * 103 is written in scientific notation.
 1.7.4: 7 * 105
 1.7.5: 7.16 * 106
 1.7.6: 8.17 * 106
 1.7.7: 1.4 * 100
 1.7.8: 2.4 * 100
 1.7.9: 7.9 * 101
 1.7.10: 2.4 * 100
 1.7.11: 4.15 * 103
 1.7.12: 3.14 * 103
 1.7.13: 6.00001 * 1010
 1.7.14: 7.00001 * 1010
 1.7.15: 32,000
 1.7.16: 64,000
 1.7.17: 638,000,000,000,000,000
 1.7.18: 579,000,000,000,000,000
 1.7.19: 317
 1.7.20: 326
 1.7.21: 5716
 1.7.22: 3829
 1.7.23: 0.0027
 1.7.24: 0.0083
 1.7.25: 0.00000000504
 1.7.26: 0.00000000405
 1.7.27: 0.007
 1.7.28: 0.005
 1.7.29: 3.14159
 1.7.30: 2.71828
 1.7.31: (3 * 104 )(2.1 * 103 )
 1.7.32: (2 * 104 )(4.1 * 103 )
 1.7.33: (1.6 * 1015 )(4 * 1011 )
 1.7.34: (1.4 * 1015 )(3 * 1011 )
 1.7.35: (6.1 * 108 )(2 * 104 )
 1.7.36: (5.1 * 108 )(3 * 104 )
 1.7.37: (4.3 * 108 )(6.2 * 104 )
 1.7.38: (8.2 * 108 )(4.6 * 104 )
 1.7.39: 8.4 * 108 4 * 105
 1.7.40: 6.9 * 108 3 * 105
 1.7.41: 3.6 * 104 9 * 102
 1.7.42: 1.2 * 104 2 * 102
 1.7.43: 4.8 * 102 2.4 * 106
 1.7.44: 7.5 * 102 2.5 * 106
 1.7.45: 2.4 * 102 4.8 * 106
 1.7.46: 1.5 * 102 3 * 106
 1.7.47: 480,000,000,000 0.00012
 1.7.48: 282,000,000,000 0.00141
 1.7.49: 0.00072 * 0.003 0.00024
 1.7.50: 66,000 * 0.001 0.003 * 0.002
 1.7.51: (2 * 105 )x = 1.2 * 109
 1.7.52: (3 * 10 2 )x = 1.2 * 104
 1.7.53: x 2 * 108 = 3.1 * 105
 1.7.54: x 5 * 1011 = 2.9 * 103
 1.7.55: x  (7.2 * 1018 ) = 9.1 * 1018
 1.7.56: x  (5.3 * 1016 ) = 8.4 * 1016
 1.7.57: (1.2 * 103 )x = (1.8 * 104 )(2.4 * 106 )
 1.7.58: (7.8 * 104 )x = (3.9 * 107 )(6.8 * 105 )
 1.7.59: How much is Bill Gates worth?
 1.7.60: How much is Warren Buffet worth?
 1.7.61: Although he is not among the top five, Mark Zuckerberg, Facebook CE...
 1.7.62: By how much does Larry Ellisons worth exceed that of Sheldon Adelson?
 1.7.63: Find the number of hot dogs consumed by each American in a year.
 1.7.64: If the consumption of Big Macs was divided evenly among all America...
 1.7.65: How many chickens are raised for food each second in the United Sta...
 1.7.66: How many chickens are eaten per year in the United States? Express ...
 1.7.67: a. What was the average per person benefit for Social Security? Exp...
 1.7.68: a. What was the average per person benefit for the food stamps prog...
 1.7.69: Medicaid provides health insurance for the poor. Medicare provides ...
 1.7.70: The area of Alaska is approximately 3.66 * 108 acres. The state was...
 1.7.71: The mass of one oxygen molecule is 5.3 * 1023 gram. Find the mass ...
 1.7.72: The mass of one hydrogen atom is 1.67 * 1024 gram. Find the mass o...
 1.7.73: In Exercises 6566, we used 3.2 * 107 as an approximation for the nu...
 1.7.74: How do you know if a number is written in scientific notation?
 1.7.75: Explain how to convert from scientific to decimal notation and give...
 1.7.76: Explain how to convert from decimal to scientific notation and give...
 1.7.77: Describe one advantage of expressing a number in scientific notatio...
 1.7.78: Use a calculator to check any three of your answers in Exercises 114.
 1.7.79: Use a calculator to check any three of your answers in Exercises 1530.
 1.7.80: Use a calculator with an EE or EXP key to check any four of your co...
 1.7.81: For a recent year, total tax collections in the United States were ...
 1.7.82: I just finished reading a book that contained approximately 1.04 * ...
 1.7.83: If numbers in the form a * 10n are listed from least to greatest, v...
 1.7.84: When expressed in scientific notation, 58 million and 58 millionths...
 1.7.85: 534.7 = 5.347 * 103
 1.7.86: 8 * 1030 4 * 105 = 2 * 1025
 1.7.87: (7 * 105 ) + (2 * 103 ) = 9 * 102
 1.7.88: (4 * 103 ) + (3 * 102 ) = 43 * 102
 1.7.89: The numbers 8.7 * 1025 , 1.0 * 1026 , 5.7 * 1026 , and 3.7 * 1027 a...
 1.7.90: 5.6 * 1013 + 3.1 * 1013
 1.7.91: 8.2 * 1016 + 4.3 * 1016
 1.7.92: Our hearts beat approximately 70 times per minute. Express in scien...
 1.7.93: Give an example of a number where there is no advantage in using sc...
 1.7.94: Simplify: 9(10x  4)  (5x  10). (Section 1.2, Example 14)
 1.7.95: Solve: 4x  1 10 = 5x + 2 4  4. (Section 1.4, Example 4)
 1.7.96: Simplify: (8x4y3 ) 2 . (Section 1.6, Example 7)
 1.7.97: Here are two sets of ordered pairs: set 1: {(1, 5), (2, 5)} set 2: ...
 1.7.98: Evaluate r 3  2r 2 + 5 for r = 5.
 1.7.99: Evaluate 5x + 7 for x = a + h.
Solutions for Chapter 1.7: Scientific Notation
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 1.7: Scientific Notation
Get Full SolutionsChapter 1.7: Scientific Notation includes 99 full stepbystep solutions. Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934. Since 99 problems in chapter 1.7: Scientific Notation have been answered, more than 9666 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).
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