Convert 0.72¯¯¯¯¯ to a rational number in simplest form.(1 point)
To convert 0.72¯¯¯¯¯ to a rational number in simplest form, we need to understand that the bar over the 2 indicates that the digit 2 repeats infinitely.
We can represent 0.72¯¯¯¯¯ as follows:
Let x = 0.72¯¯¯¯¯
Then, 100x = 72.72¯¯¯¯¯
Now, we can subtract the equations:
100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72
Dividing both sides by 99:
x = 72/99
To simplify this fraction, we can find the greatest common divisor (GCD) of 72 and 99, which is 9.
Dividing both numerator and denominator by 9:
x = 8/11
Therefore, the rational representation of 0.72¯¯¯¯¯ in simplest form is 8/11.
Which of the following is a rational number between 5 and 5 1/4?(1 point)
Responses
26−−√
start root 26 end root
517
5 Start Fraction 1 over 7 end fraction
513
5 Start Fraction 1 over 3 end fraction
525
To find a rational number between 5 and 5 1/4, we first need to convert 5 1/4 to an improper fraction.
5 1/4 = 5 + 1/4 = 20/4 + 1/4 = 21/4
Now we can find a rational number between 5 and 21/4 by taking their average:
(5 + 21/4) / 2 = (20/4 + 21/4) / 2 = 41/8
Therefore, the rational number between 5 and 5 1/4 is 41/8.
None of the given options (26−−√, 517, 513, 525) are equal to 41/8.
Which of the following is a rational number between 5 and 514?(1 point)
Responses
26−−√
5 1/7
5 1/3
5 2/5
To find a rational number between 5 and 514, we can take their average:
(5 + 514) / 2 = 519 / 2 = 259.5
However, none of the given options (26−−√, 5 1/7, 5 1/3, 5 2/5) are equal to 259.5.
Therefore, there is no rational number between 5 and 514 among the given options.
Which of the following is a rational number between 5 and 5 1/4?(1 point)
26−−√
5 1/7
5 1/3
5 2/5
To find a rational number between 5 and 5 1/4, we can take their average:
(5 + 5 1/4) / 2 = (20/4 + 21/4) / 2 = 41/8
Therefore, the rational number between 5 and 5 1/4 is 41/8.
Among the given options, the rational number 5 1/7 is the closest to 41/8. Therefore, the correct answer is 5 1/7.
What is a rational number with a denominator of 7 that is between 7–√ and 8–√. Write your answer as an improper fraction.(1 point)
To find a rational number with a denominator of 7 that is between 7–√ and 8–√, we need to find the decimal approximation of the given numbers and then convert it into a fraction with a denominator of 7.
Approximating the square roots:
√7 ≈ 2.65
√8 ≈ 2.83
So, we are looking for a rational number between 2.65 and 2.83.
To convert the decimal approximation to a fraction with a denominator of 7, we can multiply both the numerator and denominator by 100 (to clear the decimal):
2.65 = 265/100 = 53/20
2.83 = 283/100 = 283/100
Now, we can find a rational number between 53/20 and 283/100. Let's take their average:
(53/20 + 283/100) / 2 = (5300/200 + 566/200) / 2 = 5866/200
Therefore, a rational number with a denominator of 7 between 7–√ and 8–√ is 5866/200, or simplifying the fraction, 2933/100.
Describe the relationship between rational numbers and whole numbers. Are all rational numbers also whole numbers? Are all whole numbers also rational numbers? Give examples to support your answer.
Rational numbers and whole numbers are related but not interchangeable.
A rational number can be written as the ratio of two integers, where the denominator is not zero. This includes fractions, terminating decimals, and repeating decimals. Some examples of rational numbers are 1/2, 0.75, and 0.6¯¯¯¯¯.
On the other hand, whole numbers include all the positive integers (1, 2, 3, ...) and zero. Whole numbers do not include fractions or decimals. Examples of whole numbers are 0, 1, and 5.
It is important to note that not all rational numbers are whole numbers. For example, the rational number 3/2 is not a whole number because it is not an integer.
However, all whole numbers are rational numbers. This is because a whole number can be written as the ratio of itself divided by 1. For example, 5 can be written as 5/1, making it a rational number.
In summary, while all whole numbers are rational numbers, not all rational numbers are whole numbers.
Article 1 informs readers about the benefits of hand washing, and Article 2 persuades readers to wash their hands more. Given this information, which method of writing is different between the two articles?(1 point)
Responses
tone
tone
text organization
text organization
purpose for writing
purpose for writing
topic
Given the information provided, the method of writing that is different between the two articles is the purpose for writing.
Article 1 informs readers about the benefits of hand washing, which suggests an informative or educational purpose.
Article 2, on the other hand, persuades readers to wash their hands more, which indicates a persuasive or convincing purpose.
Therefore, the purpose for writing is different between the two articles.
what do i choose
Based on the response provided, you should choose "purpose for writing" as the method of writing that is different between the two articles.
What is text organization?(1 point)
Responses
the attitude of a writer toward a subject or an audience
the attitude of a writer toward a subject or an audience
the style in which an author is writing
the style in which an author is writing
the method an author uses to present information in writing
the method an author uses to present information in writing
the reason an author is writing