 31.1: Write the word name for the decimal. 0.582
 31.2: Write the word name for the decimal. 0.21
 31.3: Write the word name for the decimal. 1.0009
 31.4: Write the word name for the decimal. 2.83
 31.5: Write the word name for the decimal. 782.07
 31.6: Write the number that represents the decimal. Thirtyfive hundredths
 31.7: Write the number that represents the decimal. Three hundred twelve ...
 31.8: Write the number that represents the decimal. Sixty and twentyeigh...
 31.9: Write the number that represents the decimal. Five and three hundre...
 31.10: Round to the nearest dollar $493.91
 31.11: Round to the nearest dollar $785.03
 31.12: Round to the nearest dollar $19.80
 31.13: Round to the nearest cent $0.5239
 31.14: Round to the nearest cent $21.09734
 31.15: Round to the nearest cent $32,048.87219
 31.16: Round to the nearest tenth. 42.3784
 31.17: Round to the nearest tenth. 17.03752
 31.18: Round to the nearest tenth. 4.293
 31.19: TelSales, Inc., a prepaid phone card company in Oklahoma City, sel...
 31.20: Destiny Telecom of Oakland, California, introduced a Braille prepai...
 31.21: GameStop reported a quarterly gross margin of 839.18 dollars in mil...
 31.22: Gannett Company reported a quarterly income before tax of negative ...
Solutions for Chapter 31: DECIMALS AND THE PLACEVALUE SYSTEM
Full solutions for Business Math,  9th Edition
ISBN: 9780135108178
Solutions for Chapter 31: DECIMALS AND THE PLACEVALUE SYSTEM
Get Full SolutionsChapter 31: DECIMALS AND THE PLACEVALUE SYSTEM includes 22 full stepbystep solutions. This textbook survival guide was created for the textbook: Business Math, , edition: 9. Business Math, was written by and is associated to the ISBN: 9780135108178. This expansive textbook survival guide covers the following chapters and their solutions. Since 22 problems in chapter 31: DECIMALS AND THE PLACEVALUE SYSTEM have been answered, more than 10544 students have viewed full stepbystep solutions from this chapter.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

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

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Solvable system Ax = b.
The right side b is in the column space of A.

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

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

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.