QuestionSome square roots, like $\sqrt{13}$ , can't be expressed exactly. Why is it okay to round $\sqrt{13}$ to a decimal?

Studdy Solution

STEP 1

Assumptions1. We are dealing with the square root of13, which is an irrational number. . We are looking for a decimal approximation of $\sqrt{13}$ .
3. The concept of rounding is understood.

STEP 2

First, let's understand what an irrational number is. An irrational number is a number that cannot be expressed as a simple fraction. It's decimal representation neither ends (like1/2 =0.5) nor becomes periodic (like1/ =0.33333...). Examples of irrational numbers include $\sqrt{2}$ , $\sqrt{}$ , $\pi$ , etc.

STEP 3

The square root of13 is an irrational number. This means that its decimal representation is non-terminating and non-repeating. If we try to calculate it, we get a long string of digits that do not repeat in a pattern.
$\sqrt{13} \approx3.605551275463989...$

STEP 4

In many practical situations, we need to use a decimal approximation of irrational numbers. This is because it's often impossible or impractical to use the exact value. For example, if you're using this number in a calculation, you can't write down an infinite number of digits.

STEP 5

Rounding is a process that allows us to use a number that is "close enough" to the exact value. It makes the number easier to work with. For example, if we round $\sqrt{13}$ to two decimal places, we get3.61.

STEP 6

The appropriateness of rounding depends on the context. In many cases, the difference between the exact value and the rounded value is so small that it doesn't affect the final result significantly. However, in high precision calculations, such small differences can be important.

STEP 7

In conclusion, it's appropriate to round the square root of13 to a decimal value because it's an irrational number with a non-terminating and non-repeating decimal representation. Rounding gives us a number that is easier to work with and "close enough" to the exact value for most practical purposes.

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QuestionSome square roots, like $\sqrt{13}$ , can't be expressed exactly. Why is it okay to round $\sqrt{13}$ to a decimal?

Studdy Solution

STEP 1

Assumptions1. We are dealing with the square root of13, which is an irrational number. . We are looking for a decimal approximation of $\sqrt{13}$ .
3. The concept of rounding is understood.

STEP 2

STEP 3

The square root of13 is an irrational number. This means that its decimal representation is non-terminating and non-repeating. If we try to calculate it, we get a long string of digits that do not repeat in a pattern.
$\sqrt{13} \approx3.605551275463989...$

STEP 4

In many practical situations, we need to use a decimal approximation of irrational numbers. This is because it's often impossible or impractical to use the exact value. For example, if you're using this number in a calculation, you can't write down an infinite number of digits.

STEP 5

Rounding is a process that allows us to use a number that is "close enough" to the exact value. It makes the number easier to work with. For example, if we round $\sqrt{13}$ to two decimal places, we get3.61.

STEP 6

The appropriateness of rounding depends on the context. In many cases, the difference between the exact value and the rounded value is so small that it doesn't affect the final result significantly. However, in high precision calculations, such small differences can be important.

STEP 7

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QuestionSome square roots, like 13\sqrt{13}13​, can't be expressed exactly. Why is it okay to round 13\sqrt{13}13​ to a decimal?

Studdy Solution

STEP 1

Assumptions1. We are dealing with the square root of13, which is an irrational number. . We are looking for a decimal approximation of 13\sqrt{13}13​.3. The concept of rounding is understood.

STEP 2

STEP 3

STEP 4

In many practical situations, we need to use a decimal approximation of irrational numbers. This is because it's often impossible or impractical to use the exact value. For example, if you're using this number in a calculation, you can't write down an infinite number of digits.

STEP 5

Rounding is a process that allows us to use a number that is "close enough" to the exact value. It makes the number easier to work with. For example, if we round 13\sqrt{13}13​ to two decimal places, we get3.61.

STEP 6

The appropriateness of rounding depends on the context. In many cases, the difference between the exact value and the rounded value is so small that it doesn't affect the final result significantly. However, in high precision calculations, such small differences can be important.

STEP 7

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSome square roots, like $\sqrt{13}$ , can't be expressed exactly. Why is it okay to round $\sqrt{13}$ to a decimal?

Assumptions1. We are dealing with the square root of13, which is an irrational number. . We are looking for a decimal approximation of $\sqrt{13}$ .
3. The concept of rounding is understood.

Rounding is a process that allows us to use a number that is "close enough" to the exact value. It makes the number easier to work with. For example, if we round $\sqrt{13}$ to two decimal places, we get3.61.