3/19/2021 Sophia :: Welcome
Score 20/21
You passed this Milestone
20 questions were answered correctly.
UNIT 1 — MILESTONE 1
1 question was answered incorrectly.
1
Consider the following set of real numbers:
Which of the following lists all of the rational numbers in the set?
RATIONALE
Rational numbers can be expressed as a ratio of two integers, and are characterized by either terminating or repeating decimal patterns,
such as 0.375 or 0.3333... Irrational numbers are characterized by a non-terminating, non-repeating decimal pattern. Evaluate each
number and determine whether it is rational or irrational.
Irrational: evaluates to -1.41421... and has a non-terminating, non-repeating decimal pattern.
Rational: This is a ratio of 2 integers, -3 and 5.
Rational: This is an integer.
Rational: This has a repeating decimal pattern.
Irrational: evaluates to 2.236067... and has a non-terminating, non-repeating decimal pattern.
Rational: The digits terminate after the 9 in the tenths place.
The rational numbers in the set are .
CONCEPT
Real Number Types
2
Write the following expression as a single integer.
21 – (-17) – 15
-19
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, 3/19/2021 Sophia :: Welcome
23
53
-11
RATIONALE
We first will evaluate the subtraction from left to right. Begin by evaluating 21 minus negative 17. Subtracting a negative number is equivalent to
adding its opposite: so 21 – (-17) is the same as 21 + 17.
21 plus 17 equals 38. Next, subtract 15 from 38.
38 minus 15 equals 23.
CONCEPT
Adding and Subtracting Positive and Negative Numbers
3
Tyler spent 17,700 seconds completing a 1,000 piece puzzle.
How many hours is this equivalent to? Answer choices are rounded to the nearest hour.
5 hours
20 hours
124 hours
288 hours
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 seconds to
hours. We might not know off-hand how many seconds are in an hour, but we know how many seconds are in a
minute, and how many minutes are in an hour. We will use these facts to set up conversion factors.
There are 60 minutes in 1 hour and 60 seconds in 1 minute. To convert 17700 seconds into hours, multiply
by the fractions and .
Notice how the fractions are set up. The units of seconds and minutes will cancel, leaving only hours. Finally we
can evaluate the multiplication by multiplying across the numerator and denominator.
In the denominator, 60 times 60 equals 3600. 17700 divided by 3600 is approximately 4.92. Rounded to the nearest
hour, 17700 seconds is equivalent to 5 hours.
CONCEPT
Converting Units
4
What is the following expression equivalent to?
https://snhu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/8316668 2/15
Score 20/21
You passed this Milestone
20 questions were answered correctly.
UNIT 1 — MILESTONE 1
1 question was answered incorrectly.
1
Consider the following set of real numbers:
Which of the following lists all of the rational numbers in the set?
RATIONALE
Rational numbers can be expressed as a ratio of two integers, and are characterized by either terminating or repeating decimal patterns,
such as 0.375 or 0.3333... Irrational numbers are characterized by a non-terminating, non-repeating decimal pattern. Evaluate each
number and determine whether it is rational or irrational.
Irrational: evaluates to -1.41421... and has a non-terminating, non-repeating decimal pattern.
Rational: This is a ratio of 2 integers, -3 and 5.
Rational: This is an integer.
Rational: This has a repeating decimal pattern.
Irrational: evaluates to 2.236067... and has a non-terminating, non-repeating decimal pattern.
Rational: The digits terminate after the 9 in the tenths place.
The rational numbers in the set are .
CONCEPT
Real Number Types
2
Write the following expression as a single integer.
21 – (-17) – 15
-19
https://snhu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/8316668 1/15
, 3/19/2021 Sophia :: Welcome
23
53
-11
RATIONALE
We first will evaluate the subtraction from left to right. Begin by evaluating 21 minus negative 17. Subtracting a negative number is equivalent to
adding its opposite: so 21 – (-17) is the same as 21 + 17.
21 plus 17 equals 38. Next, subtract 15 from 38.
38 minus 15 equals 23.
CONCEPT
Adding and Subtracting Positive and Negative Numbers
3
Tyler spent 17,700 seconds completing a 1,000 piece puzzle.
How many hours is this equivalent to? Answer choices are rounded to the nearest hour.
5 hours
20 hours
124 hours
288 hours
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 seconds to
hours. We might not know off-hand how many seconds are in an hour, but we know how many seconds are in a
minute, and how many minutes are in an hour. We will use these facts to set up conversion factors.
There are 60 minutes in 1 hour and 60 seconds in 1 minute. To convert 17700 seconds into hours, multiply
by the fractions and .
Notice how the fractions are set up. The units of seconds and minutes will cancel, leaving only hours. Finally we
can evaluate the multiplication by multiplying across the numerator and denominator.
In the denominator, 60 times 60 equals 3600. 17700 divided by 3600 is approximately 4.92. Rounded to the nearest
hour, 17700 seconds is equivalent to 5 hours.
CONCEPT
Converting Units
4
What is the following expression equivalent to?
https://snhu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/8316668 2/15
