Which of the following is a rational number?(1 point)
Responses
88√
the fraction with numerator 8 and denominator square root of 8
7–√
square root of 7
7.8
7.8
π
7.8
How do you write 14 programming errors for every 56 programmers as a rational number? Select the rational number that represents this scenario. (1 point)
To write 14 programming errors for every 56 programmers as a rational number, we need to express it as a fraction.
The ratio of 14 programming errors to 56 programmers can be written as 14/56.
Simplifying this fraction, we can divide both the numerator and denominator by 14:
14/56 = 1/4
Therefore, the rational number that represents this scenario is 1/4.
Use a calculator to determine if 78 is a rational number. (1 point)
Responses
The decimal equivalent of 78 is 0.875. This number is a terminating decimal. It is a rational number.
The decimal equivalent of Start Fraction 7 over 8 End Fraction is 0.875. This number is a terminating decimal. It is a rational number.
The decimal equivalent of 78 is 0.875. This number is a repeating decimal. It is a rational number.
The decimal equivalent of Start Fraction 7 over 8 End Fraction is 0.875. This number is a repeating decimal. It is a rational number.
The decimal equivalent of 78 is 0.875. This number is a terminating decimal. It is not a rational number.
The decimal equivalent of Start Fraction 7 over 8 End Fraction is 0.875. This number is a terminating decimal. It is not a rational number.
The decimal equivalent of 78 is 1.14285714285714. This number is a terminating decimal. It is a rational number.
The decimal equivalent of Start Fraction 7 over 8 End Fraction is 1.14285714285714. This number is a terminating decimal. It is a rational number.
The decimal equivalent of 78 is 0.875. This number is a terminating decimal. It is a rational number.
The rational number among the given options is the fraction with numerator 8 and denominator square root of 8.
To determine which of the given options is a rational number, we need to understand what a rational number is. A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.
Let's analyze each option:
1. 88√: This is an irrational number since it involves the square root of a non-perfect square number (88).
2. The fraction with numerator 8 and denominator √8: To determine if this is a rational number, we need to simplify the fraction. Simplifying the denominator, we have √8 = √(4 * 2) = √4 * √2 = 2√2.
Therefore, the fraction is 8 / 2√2 = (8 * √2) / (2 * 2) = 4√2 / 2 = 2√2.
Since 2√2 can be expressed as the quotient of two integers (2 and √2 can be rationalized as 2√2), it is a rational number.
3. 7–√: This is an irrational number since it involves the square root of a non-perfect square number (7).
4. 7.8: This is a rational number since it can be expressed as the quotient of two integers. We can rewrite 7.8 as 78/10, which is the fraction form of the decimal number. Therefore, 7.8 is rational.
5. π (pi): This is an irrational number since it cannot be expressed as the quotient of two integers. Pi is a transcendental number and goes on indefinitely without repeating or terminating.
Based on these explanations, the rational numbers among the options are the fraction with numerator 8 and denominator √8 and 7.8.