Asked by Needapass

Using a number line, what whole number and rational number to the nearest half is square root 40 between
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Using a number line, what whole number and ration number to the nearest half is square root 58 between
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Using rational approximations what is an inequality statement comparing square root 81 and square root 88. Enter <,> or =
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Write 6,739 in expanded form
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Express 8/11 as a repeating decimal. Mark the cycle of repeating digits with a bar
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Convert 0.72 (repeating) to a ration number in simplest form
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Which of the following is a rational number between 5 and 5 1/4
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The answers to the question are
5 1/7
Square root 26
5 2/5
5 1/3
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Pick one please
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What is a ration number with a denominator of 7 that is between square root 7 and square root 8. Write your answer as an improper fraction
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Describe the relationship between rational numbers and whole numbers. Are all rational numbers also whole number? Are all whole numbers also ration numbers? Give examples to support your answer.
Answered by GPT-4
The square root of 40 is approximately 6.32. So on a number line, it's between the whole numbers 6 and 7. Rounding to the nearest half, it's also between 6.5 and 6.
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The square root of 58 is approximately 7.62. So on a number line, it's between the whole numbers 7 and 8. Rounding to the nearest half, it's also between 7.5 and 8.
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The square root of 81 is exactly 9, and the square root of 88 is approximately 9.38. So, √81 < √88.
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The expanded form of 6,739 is 6000 + 700 + 30 + 9.
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The decimal representation of 8/11 is 0.72 (repeating). So, marking the repeating digits with a bar, it is written as 0.72.
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The decimal 0.72 (repeating) converts to the rational number 8/11 in simplest form.
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A rational number between 5 and 5 1/4 would be 5.1, 5.2, or 5.125, among many others.
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Out of the choices given, 5 1/7, 5 1/3, and 5 2/5 are rational numbers between 5 and 5 1/4. The square root of 26 is not a rational number between 5 and 5 1/4.
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Sure, let's go with 5 1/7.
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The square root of 7 is approximately 2.65 and the square root of 8 is approximately 2.83. A rational number with a denominator of 7 that falls between these two values could be 19/7 which is approximately 2.71.
Answered by GPT-4
Rational numbers and whole numbers are both types of numbers that we use in arithmetic, but they are different types of numbers.

Whole numbers are a subset of the rational numbers. They are the simplest type of numbers and include zero and all the positive integers (numbers without fractional or decimal parts), for example, 0, 1, 2, 3, 4, 5, and so on.

On the other hand, rational numbers are numbers that can be expressed as a ratio of two integers, where the denominator is not zero. They can be positive or negative and they can be written as fractions, decimals or whole numbers. For example, 1/2, 3.75, -6, and 0 are all rational numbers.

So to answer your questions:

- Not all rational numbers are whole numbers. For example, 1/2 is a rational number, but it's not a whole number because it has a fractional part.

- However, all whole numbers can be considered as rational numbers because they can be expressed as a ratio of two integers. For example, the whole number 3 can be expressed as the ratio 3/1, which makes it a rational number. So, yes, all whole numbers are also rational numbers.