1.
Generally, the order of magnitude of a number is the smallest power of ... required to represent that number.
Correct Answer
A. 10
Explanation
The order of magnitude of a number represents the scale of that number. In this case, the correct answer is 10 because it is the smallest power of 10 required to represent the number. This means that the number is in the range of 10 to 99, as the next order of magnitude would be 100.
2.
If values differ by two orders of magnitude, they differ by a factor of about ....
Correct Answer
D. 100
Explanation
If values differ by two orders of magnitude, it means that one value is 100 times greater or smaller than the other value. This is because each order of magnitude represents a factor of 10. Therefore, the correct answer is 100, as it represents the factor by which the values differ.
3.
The larger value is less than ..... the smaller value.
Correct Answer
B. Ten times
Explanation
The correct answer is "ten times" because when a larger value is "ten times" less than a smaller value, it means that the larger value is significantly smaller in comparison. In other words, the larger value is only one-tenth of the smaller value.
4.
In the context of order of magnitude, what does it mean when we say an estimate is "one order of magnitude larger" than another?
Correct Answer
B. The estimate is approximately 10 times larger.
Explanation
When we say that one quantity is "one order of magnitude larger" than another, we mean that it is approximately 10 times larger. In scientific notation, an order of magnitude is a power of 10. So, if something is one order of magnitude larger, it's roughly 10 times greater. For example, if you have a value of 100 and you say that another value is one order of magnitude larger, it would be around 1000 (10 times 100), not exactly 1000, but in the same ballpark. This concept is commonly used in science and engineering to provide rough estimates and comparisons between values that differ significantly in scale.
5.
Order-of-magnitude differences are called ...... when measured on a logarithm scale.
Correct Answer
B. Decades
Explanation
Order-of-magnitude differences are called "decades" when measured on a logarithm scale. This is because a logarithm scale allows for the representation of large differences in values by using powers of 10. Each increase of one unit on the logarithm scale represents a multiplication by 10. Therefore, when there is an order-of-magnitude difference between values, it means that one value is ten times larger or smaller than the other. In the context of the question, "decades" is the correct answer as it represents a difference of approximately ten times on a logarithm scale.
6.
An order-of-magnitude difference between two values is a factor of ...
Correct Answer
A. 10
Explanation
An order-of-magnitude difference between two values is a factor of 10. This means that one value is 10 times greater or smaller than the other value. For example, if one value is 100 and the other is 1000, there is an order-of-magnitude difference of 10 between them. Similarly, if one value is 0.01 and the other is 0.1, there is also an order-of-magnitude difference of 10 between them.
7.
The ancient Greeks ranked the nighttime brightness of celestial bodies by how many levels?
Correct Answer
C. 6 levels
Explanation
The ancient Greeks ranked the nighttime brightness of celestial bodies by six levels. This ranking system was known as the Magnitude Scale, with the brightest objects being assigned a magnitude of 1 and the faintest objects being assigned a magnitude of 6. This scale was based on the apparent brightness of the celestial bodies as observed from Earth. The lower the magnitude number, the brighter the object appeared in the night sky. This system allowed the Greeks to categorize and compare the brightness of different celestial bodies.
8.
An order-of-magnitude estimate of a variable, whose precise value is unknown, is an estimate rounded to the nearest power of ....
Correct Answer
B. Ten
Explanation
An order-of-magnitude estimate is an approximation of a variable's value that is rounded to the nearest power of ten. This means that the estimate is rounded up or down to the nearest multiple of ten, such as 10, 100, 1000, etc. This allows for a quick and rough estimation of the variable's value without needing to know the precise value.
9.
Who is not a scientist among them?
Correct Answer
D. Will Smith
Explanation
Will Smith is not a scientist among them because he is primarily known as an actor and musician, not for his contributions to scientific research or knowledge. Isaac Newton and Albert Einstein are renowned physicists who made significant advancements in the field of science. Bill Nye, also known as "The Science Guy," is a science educator and television host who promotes scientific literacy. However, Will Smith is not known for his scientific expertise or contributions.
10.
What is the order of magnitude of 7.8×10^{3}÷2.5×10^{2}?
Correct Answer
A. 10