How many digits long could the repeating cycle of a repeating decimal be if the denominator of the rational number is 7?
The repeating cycle of a decimal with denominator 7 can have at most 6 digits.
This is because when we divide any number by 7, the remainder can only range from 0 to 6 (since 7 divides evenly into 7 once with a remainder of 0).
So, when we have a fraction with denominator 7, the decimal representation will repeat at most every 6 digits.
Convert 0.27¯¯¯¯¯ to a rational number in simplest form
To convert the recurring decimal 0.27¯¯¯¯¯ to a rational number in simplest form, we let x = 0.27¯¯¯¯¯ and then subtract the non-recurring part of the decimal to eliminate the repetition.
Let's multiply both sides of the equation x = 0.27¯¯¯¯¯ by 100 to shift the decimal point two spots to the right:
100x = 27.27¯¯¯¯¯
Now, let's subtract the original equation from the new one:
100x - x = 27.27¯¯¯¯¯ - 0.27¯¯¯¯¯
This simplifies to:
99x = 27 (since the recurring parts cancel out: 27.27¯¯¯¯¯ - 0.27¯¯¯¯¯ = 27)
Now, to get x by itself, we divide both sides of the equation by 99:
x = 27/99
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 9:
x = (27 ÷ 9) / (99 ÷ 9)
x = 3/11
Therefore, 0.27¯¯¯¯¯ is equal to the rational number 3/11 in simplest form.
Which of the following is the role of supporting details in a text?
The role of supporting details in a text is to provide evidence or examples that strengthen or clarify the main ideas or claims being made. Supporting details help to support the main points of the text and provide additional information or explanation to ensure that the reader understands the author's message or argument. These details may include facts, statistics, anecdotes, examples, or expert opinions that help to reinforce the main ideas and make the text more informative and persuasive.
Use the paragraph to answer the question.
One impressive cave system is the lava tube caves of Lava Beds National Monument. The caves provide a safe habitat for millions of bats. In order to visit the caves, visitors must first be screened for white-nose syndrome. It is a disease that is fatal to bats.
Which option best identifies the central idea of the paragraph?
The central idea of the paragraph is the lava tube caves of Lava Beds National Monument and their importance as a safe habitat for millions of bats, while also highlighting the need to screen visitors for white-nose syndrome, a disease that is fatal to bats.
When you tell the most important part of a text, what are you identifying?
When you identify the most important part of a text, you are typically identifying the main idea or central idea of the text. This is the overriding theme or message that the author is trying to convey to the reader. The main idea encapsulates the primary focus or purpose of the text and serves as a guide for understanding the supporting details and arguments presented by the author.
Use the paragraph to answer the question.
About 1.5 million species of fungi exist on Earth. They act as nature’s decomposers. These organisms break down matter and release enzymes and acids that unlock nutrients for plants and soil organisms. You may be familiar with macrofungi, a type of fungus that includes mushrooms. But for the most part, fungi exist as mycelia, tiny threads that snake underground in billions of interconnected threads. They twist and twine with tree root systems, helping tress obtain crucial nutrients. Mycologists call these networks of mycelia "Earth’s nervous system."
Which statement best identifies the central idea of the paragraph?