 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 26034 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.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

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.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

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.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(DÂ» O.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

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

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

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.