Question

Marla works at a manufacturing plant making well pumps. She needs to set a gauge on one of her machines so it precisely measures one of the fittings. She has found that setting the gauge at 4.657 is not enough, but setting the gauge to 4.658 is too much. What should she set the gauge at so it gives the result she wants?(1 point)
Responses

4.65
4.65

4.6582
4.6582

4.6570
4.6570

4.6578
4.6578

Answer 1

What are three irrational numbers between 15−−√
15
and 30−−√
30
?(1 point)
Responses

17 −−−√
17

, 21−−√
21
, 27−−√
27
Start Root 17 End Root , Start Root 21 End Root , Start Root 27 End Root

4, 18−−√
18
, 19−−√
19
4, Start Root 18 End Root , Start Root 19 End Root

20 −−−√
20

, 22−−√
22
, 25−−√
25
Start Root 20 End Root , Start Root 22 End Root , Start Root 25 End Root

16 −−−√
16

, 17−−√
17
, 18−−√

Answer 2

Using the numbers 3.14 and π
𝜋
as examples, describe the difference between rational and irrational numbers in 1–2 sentences.(2 points)

Answer 3

Marla should set the gauge at **4.6578**. This is a value that is higher than 4.657 but lower than 4.658, which fits her requirement for precise measurement.

Answer 4

To find three irrational numbers between \( \sqrt{15} \) and \( \sqrt{30} \), we first determine approximate values for these square roots:

- \( \sqrt{15} \approx 3.87 \)
- \( \sqrt{30} \approx 5.48 \)

We can choose irrational numbers that fall between these two values.

From the provided options, the correct response that contains three irrational numbers between \( \sqrt{15} \) and \( \sqrt{30} \) is:

**Start Root 17 End Root , Start Root 21 End Root , Start Root 27 End Root**
\( \sqrt{17} \), \( \sqrt{21} \), and \( \sqrt{27} \) are all between \( \sqrt{15} \) and \( \sqrt{30} \).

Answer 5

Rational numbers, such as 3.14, can be expressed as the ratio of two integers (for example, 3.14 can be written as 314/100), while irrational numbers, like π (pi), cannot be expressed as a simple fraction and have non-repeating, non-terminating decimal expansions, making them impossible to represent as a ratio of integers. Thus, the key difference lies in whether the number can be represented as a fraction or not.