Why is π
an irrational number?
(1 point)
Responses
It is a terminating decimal.
It is a terminating decimal.
It is a nonterminating, repeating decimal.
It is a nonterminating, repeating decimal.
It is a nonterminating, nonrepeating decimal and cannot be written as a fraction.
It is a nonterminating, nonrepeating decimal and cannot be written as a fraction.
It can be written as a fraction.
The correct response is: It is a nonterminating, nonrepeating decimal and cannot be written as a fraction.
Which method will give you the greater value, rounding 38.264 to the tenths place or truncating it to one decimal place?
(1 point)
Responses
Rounding to the tenths place.
Rounding to the tenths place.
Truncating to one decimal place.
Truncating to one decimal place.
They have the same value whether you round or truncate.
The correct response is: Rounding to the tenths place.
Place the following numbers in order from least to greatest, as they would fall on a number line. - 2.0, 0.25, - 1.02, 1.98.
(1 point)
Responses
- 1.02, - 2.0, 0.25, 1.98
- 1.02, - 2.0, 0.25, 1.98
- 2.0, - 1.02, 0.25, 1.98
- 2.0, - 1.02, 0.25, 1.98
- 2.0, - 1.02, 1.98, 0.25
- 2.0, - 1.02, 1.98, 0.25
0.25, - 1.02, 1.98, - 1.02
The correct response is: - 2.0, - 1.02, 0.25, 1.98.
The correct response is: It is a nonterminating, nonrepeating decimal and cannot be written as a fraction.
π (pi) is an irrational number because it cannot be expressed as a fraction or a ratio of two integers. Its decimal representation goes on forever without repeating or terminating, which means it cannot be expressed exactly as a finite fraction. This property makes it different from rational numbers, which can be expressed as fractions.
The correct answer is "It is a nonterminating, nonrepeating decimal and cannot be written as a fraction."
To understand why π is an irrational number, we need to explain what it means for a number to be rational or irrational.
A rational number is a number that can be expressed as a fraction of two integers, where the denominator is not zero. For example, 1/2, 3/4, and -5/7 are all rational numbers.
An irrational number, on the other hand, is a number that cannot be expressed as a fraction of two integers. Instead, it has a decimal representation that goes on forever without repeating patterns.
Now, let's apply this understanding to π. π is the ratio of a circle's circumference to its diameter, and it is approximately equal to 3.14159. However, this decimal representation does not terminate (end) or repeat with a pattern. Instead, it continues indefinitely without any predictable sequence. This makes π a nonterminating, nonrepeating decimal.
Since π cannot be expressed as a fraction of two integers, it is considered an irrational number.