Mathematics, 21.08.2020 14:01, meg7211

Part A: Find a rational number that is between 7.7 and 7.9. Explain why it is rational. (2 points) I kinda understand this part, that it would be 7.8 because you can turn it into a fraction but the others you cannot but I don't know if that's correct. Part B: Find an irrational number that is between 7.7 and 7.9. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth. (3 points)

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answered: 8545548

Using the numbers sets, it is found that:

A. Examples are 7.8, 7.77777, 7.888888, 7.9777,...B. An example of an irrational number is 7.8439232320393923930932..., as it has an infinite number of decimal digits without a pattern, and rounded to the nearest hundredth, it is 7.84.Whole numbers: Also called natural, set of numbers including all positive numbers and 0, so: {0,1,2,...} Integer numbers: Number without decimals, that can be positive of negative, so: {...,-2,-1,0,1,2,} Rational numbers: Integer plus decimals that can be represented by fractions, that is, they either have a pattern, or have a finite number of decimal digits, for example, 0, 2, 0,45(finite number of decimal digits), 0.3333(3 repeating is the pattern), 0.32344594459(4459 repeating is the pattern). Irrational numbers: Decimal numbers that are not represented by patterns, that is, for example, 0.1033430290339.

Part A:

Rational, thus any number with a finite number of decimal digits, for example, 7.78, 7.79, 7.8,7.805,... or even repeating patterns in the decimals(7.77777, 7.8888888, 7.98888888)

Part B:

Irrational, thus numbers with an infinite number of decimal digits, without a pattern, for example:

7.8439232320393923930932...Rounded to the nearest hundredth, that is, two places, 7.84, as 3, which is the thousandths digit is less than 5

A similar problem is given at link

answered: ijade07

Part A: 7.8. It equals 78/10.

Part B: √61. It is about 7.8102

Step-by-step explanation:

Part A:

Yes, you are correct. I'm going to expand on your answer, however.

So, recall what rational numbers are. They are any number that cannot be written as a fraction between two integers. Another way of saying this is that if the number doesn't repeat and doesn't terminate, then it's irrational.

So, yes, 7.8 is a rational number between 7.7 and 7.9.

In fact, there are infinite rational numbers between 7.7 and 7.9. 7.8 is rational. So is 7.88. And 7.888. And 7.8888. Their fractions are, respectively: 78/10, 788/100, 7888/1000, and 78888/10000. They can all be written as a fraction (between two integers), and so, they are rational.

Part B:

So, unlike rational numbers, irrational numbers do not terminate and they do not repeat. An example is √2. Its approximation is 1.41424... This doesn't repeat nor terminate.

To find an irrational number between 7.7 and 7.9, the strategy is to square the two numbers. 7.7^2 is 59.29 and 7.9^2 is 62.41. Now, we just need to find a number within this range that when you take the square root of it, it is irrational.

After thinking, 61 is a valid candidate. The square root of 61 is 7.81024... It doesn't repeat and doesn't terminate. It is irrational.

In fact, the square root of any prime number is irrational.

And 7.81024... is between 7.7 and 7.9. Therefore, an answer we could give is √61.

And it's approximately 7.8102.

Edit: Typo

answered: Guest

nothjing

step-by-step explanation:

answered: Guest

(6,0) i hope it makes enough sense