2/5/2021 Sophia :: Welcome
Score 15/21
You passed this Milestone
15 questions were answered correctly.
UNIT 1 — MILESTONE 1
6 questions were answered incorrectly.
1
The diameter of a hydrogen atom is about meters. A protein molecule has an overall length of
2000 times (or times) the diameter of a hydrogen atom.
What is the length of the protein molecule, in meters, if it were written in scientific notation?
meters
meters
meters
meters
RATIONALE
To find the length of the protein molecule, multiply
1.04 space X space 10 to the power of short dash 10
end exponent
by 2000, which can be expressed as .
https://waldenu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7598661 1/19
,2/5/2021 Sophia :: Welcome
When multiplying numbers in scientific notation, you must
deal with the numbers and 10s separately. First, multiply 1.04
and 2.
1.04 times 2 equals 2.08. Now you can use the Product
Property of Exponents on the 10s and add the exponents.
-10 plus 3 equals -7, which is the exponent for the base 10.
Finally, combine the number part and the power of 10 together.
The length of the protein molecule (in meters), when written in
scientific notation, is .
CONCEPT
Multiplication and Division in Scientific Notation
2
Geri runs a total of 3.1 miles in a cross-country race.
How many feet is this equivalent to?
5,280 feet
15,840 feet
4,989 feet
16,368 feet
RATIONALE
In general, we use conversion factors to convert from one unit to another. A
conversion factor is a fraction with equal quantities in the numerator and
denominator, but written with different units. We want to convert miles to feet. We
know how many feet are in 1 mile. We will use this fact to set up a conversion
factor.
There are 5280 feet in 1 mile. To convert 3.1 miles into feet, multiply
by the fraction .
Notice how the fractions are set up. The units of miles will cancel, leaving only feet.
Finally we can evaluate the multiplication by multiplying across the numerator and
https://waldenu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7598661 2/19
, 2/5/2021 Sophia :: Welcome
denominator.
In the numerator, 3.1 times 5280 equals 16368. 3.1 miles is equivalent to 16,368
feet.
CONCEPT
Converting Units
3
Evaluate the following expression.
2(|-3| + |-1|)
8
-7
7
-8
RATIONALE
Evaluate each absolute value first. Absolute value is always non-negative. Rewrite the
number without any negative sign if there was one.
The absolute value of -3 is 3. The absolute value of -1 is 1. Now we can add these two
numbers
3 plus 1 is 4. Next, multiply 2 by 4.
2 times 4 is 8.
CONCEPT
Introduction to Absolute Value
4
Perform the indicated operations and write your result as a single number.
https://waldenu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7598661 3/19
Score 15/21
You passed this Milestone
15 questions were answered correctly.
UNIT 1 — MILESTONE 1
6 questions were answered incorrectly.
1
The diameter of a hydrogen atom is about meters. A protein molecule has an overall length of
2000 times (or times) the diameter of a hydrogen atom.
What is the length of the protein molecule, in meters, if it were written in scientific notation?
meters
meters
meters
meters
RATIONALE
To find the length of the protein molecule, multiply
1.04 space X space 10 to the power of short dash 10
end exponent
by 2000, which can be expressed as .
https://waldenu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7598661 1/19
,2/5/2021 Sophia :: Welcome
When multiplying numbers in scientific notation, you must
deal with the numbers and 10s separately. First, multiply 1.04
and 2.
1.04 times 2 equals 2.08. Now you can use the Product
Property of Exponents on the 10s and add the exponents.
-10 plus 3 equals -7, which is the exponent for the base 10.
Finally, combine the number part and the power of 10 together.
The length of the protein molecule (in meters), when written in
scientific notation, is .
CONCEPT
Multiplication and Division in Scientific Notation
2
Geri runs a total of 3.1 miles in a cross-country race.
How many feet is this equivalent to?
5,280 feet
15,840 feet
4,989 feet
16,368 feet
RATIONALE
In general, we use conversion factors to convert from one unit to another. A
conversion factor is a fraction with equal quantities in the numerator and
denominator, but written with different units. We want to convert miles to feet. We
know how many feet are in 1 mile. We will use this fact to set up a conversion
factor.
There are 5280 feet in 1 mile. To convert 3.1 miles into feet, multiply
by the fraction .
Notice how the fractions are set up. The units of miles will cancel, leaving only feet.
Finally we can evaluate the multiplication by multiplying across the numerator and
https://waldenu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7598661 2/19
, 2/5/2021 Sophia :: Welcome
denominator.
In the numerator, 3.1 times 5280 equals 16368. 3.1 miles is equivalent to 16,368
feet.
CONCEPT
Converting Units
3
Evaluate the following expression.
2(|-3| + |-1|)
8
-7
7
-8
RATIONALE
Evaluate each absolute value first. Absolute value is always non-negative. Rewrite the
number without any negative sign if there was one.
The absolute value of -3 is 3. The absolute value of -1 is 1. Now we can add these two
numbers
3 plus 1 is 4. Next, multiply 2 by 4.
2 times 4 is 8.
CONCEPT
Introduction to Absolute Value
4
Perform the indicated operations and write your result as a single number.
https://waldenu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7598661 3/19
