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Math 090 Exam 5 Review – Chapter 6
Remember that material from earlier exams may be on this exam also – your exams will build on
each other!
Section 6.1 Decimals: Reading, Writing, Rounding, and Inequalities
decimal point
Decimals: are another way of expressing fractions and mixed numbers. In a decimal, the decimal point
separates the whole number part from the fraction part of the number.
whole number part
fraction part
.1 =
1
 one tenth
10
.01 =
1
 one hundredth
100
.001 =
1
 one thousandth
1, 000
.0001 =
1
 one ten-thousandth
10, 000
.00001 =
1
 one hundred-thousandth
100, 000
ten-thousndths
thousandths
hundredths
tenths
ones (units)
tens
hundreds
thousands
. . .
ten thousands
.
. . .
2
Write the word name:
1. 6.7003
2. 0.524
Write the place value notation for:
3. Twenty-six and fifteen hundred-thousandths
4. Three ten-thousandths
Round to the indicated place:
5. Round to the thousandths: 0.0465
6. Round to the hundredths: 128.199
Change to fractions and simplify if needed:
7.
0.76
8. 0.008
Arrange in order from smallest to largest:
9.
6.9, 6.09, 6.19, 6.109
10.
0.011, 0.001, 0.010, 0.100
Compare using < or >:
11.
6.23_________6.203
12.
0.002__________0.01
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Section 6.2 Adding and Subtracting Decimals:
Add or subtract:
13. 6.2 + 15.305
14. 6.3x  5.41x  20.79x
15. Add 3.54 x 2  5.42 x to 7.58 x 2  2.003 x
16. 15.403x  5.267 x
17. Find the difference of 6.3302 x 3 and
18. Subtract
3.4x 1.9
Section 6.3 Multiplying Decimals
19.
3.05 0.003
from
 6.049 x3
 2.6x  2.35
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20.
1.6 x   5.7 x 2   2.5

21. 2.6 x 2 4.5 xz  6.7 x 2 z 2

22.  3.7 x  2.4  0.7 x  .5
Section 6.4 Multiplying and Dividing by Powers of Ten and Scientific Notation
A power of ten is a number that can be written as 10a where a is an integer.
Scientific Notation:
A number in scientific notation is written as the product of two numbers. The first
number is between one and ten (including one but not ten) and the second number
is a power of ten. Use an “×” to show the multiplication of the two numbers.
a 10n
1  a  10
n is an integer
**SIGN CHECK FOR EXPONENT OF 10:
If the original number is greater than 10, the exponent of 10 in scientific notation form should be
positive.
If the original number is less than 1, the exponent of 10 in scientific notation form should be
negative.
(If the original number is in between 1 and 10, the power of 10 will be 0)
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Write in scientific notation:
23. 70,400
24. 0.00574
25. 34,780,000,000
26. 0.0000061
Write in place value notation:
27. 6.275 X 106
28. 1.34 X 105
29. 3.8 X 108
Section 6.5
Dividing Decimals
Change to a decimal and round to the nearest thousandth if needed:
30.
12
57
31. 6
2
25
Divide:
32. 20.8  (3.25) 
6
33.
1.2 x 4 y 7  1.488 x 2 y 4
=
0.24 x 2 y 2
Compare using < or >:
34.
8
_________0.89
9
35.
10.85_________10
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Section 6.7 Evaluating Algebraic Expressions and Formulas with Decimals
Evaluate expressions containing decimals in the same order as with integers.
Please Excuse My Dear Aunt Sally
Or:
Parentheses
Exponents
Multiplication and Division (left to right)
Addition and Subtraction (left to right)
Evaluate:
36.
x( x  y )
when x  2.6 and y  0.4
y
7
37.  xy 2  y when x  4.2 and y  0.3 Round your answer to the nearest hundredth.
Section 6.8 Solving Equations Involving Decimals
Solve the following equations for x. Round your answer to the nearest tenth.
38. 6.7 x  3.4  6.5x  3.15
39. 12.575  4.2x  5.1 1.17 x
Geometry Reminders:
Remember that the formula for the area of a rectangle is length × width.
A  l w
The formula for the perimeter of a rectangle is (2 × length) + (2 × width)
P  2l  2w
Solve:
40. The perimeter of a rectangle is 15.4 feet. The length is 3.6 feet.
a. What is its width?
b. What is the area of the rectangle?
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Fraction Review
41. Evaluate: x 2  xy when x 
42. Solve:
1
1
and y 
3
4
2
1
x  x  x  9 Use the LCD method to eliminate the fractions!
3
6
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Answers to Math 090 Exam 5 Review
1. Six and seven thousand three tenthousandths
2. Five hundred twenty-four thousandths
29. 0.000000038
30. 0.211
31. 6.08
3. 26.00015
32. 6.4
4. 0.0003
33. 5 x 2 y 5  6.2 y 2
5. 0.047
34. <
6. 128.20
35. >
7.
19
25
36. 19.5
8.
1
125
38. x  32.8
37.  0.08
39. x  2.5
9. 6.09, 6.109, 6.19, 6.9
40. a. The width is 4.1 feet
10. 0.001, 0.010, 0.011, 0.100
11. >
7
36
42. x  6
41.
12. <
13. 21.505
14. 21.68x
15. 4.04 x 2  3.417 x
16. 20.670x
17. 12.3792x 3
18. 0.8x  0.45
19. 0.00915
3
20. 22.8x
3
4 2
21. 11.7 x z  17.42 x z
2
22. 2.59 x  0.17 x  1.2
23. 7.04 X 10
24. 5.74 X 10
4
3
10
25. 3.478 X 10
26. 6.1 X 10
b. The area is 14.76 square feet
6
27. 6,275,000
28. 0.0000134