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-31/10 ? -pi which one is less than or grater than

11 answers

To compare \(-\frac{31}{10}\) and \(-\pi\), we first need to understand their approximate numerical values.

  1. Calculate \(-\frac{31}{10}\): \[ -\frac{31}{10} = -3.1 \]

  2. Approximate \(-\pi\): The value of \(\pi\) is approximately \(3.14\), hence: \[ -\pi \approx -3.14 \]

Now we compare:

  • \(-3.1\) (which is \(-\frac{31}{10}\))
  • \(-3.14\) (which is \(-\pi\))

Since \(-3.1\) is greater than \(-3.14\) (because it is closer to zero), we have:

\[ -\frac{31}{10} > -\pi \]

In conclusion, \(-\pi\) is less than \(-\frac{31}{10}\).

ok so can u do the same thing but with new numbers

Sure! Please provide the new numbers you'd like to compare, and I'll help you determine which one is less than or greater than the other.

-pi ? -3 1/4

To compare \(-\pi\) and \(-\frac{13}{4}\) (which is the fractional form of \(-3 \frac{1}{4}\)), we first need to understand the approximate numerical values.

  1. Value of \(-\pi\): \(\pi \approx 3.14\), so: \[ -\pi \approx -3.14 \]

  2. Convert \(-3 \frac{1}{4}\) to an improper fraction: \(-3 \frac{1}{4}\) can be expressed as: \[ -\left(3 + \frac{1}{4}\right) = -\frac{12}{4} - \frac{1}{4} = -\frac{13}{4} \] Now converting it to a decimal: \[ -\frac{13}{4} = -3.25 \]

Now we compare:

  • \(-\pi \approx -3.14\)
  • \(-\frac{13}{4} = -3.25\)

Since \(-3.14\) is greater than \(-3.25\), we find that:

\[ -\pi > -3 \frac{1}{4} \]

In conclusion, \(-3 \frac{1}{4}\) is less than \(-\pi\).

ok -pi^2 ? devide 77

To compare \(-\pi^2\) and \(-\frac{77}{1}\) (or simply \(-77\)), we first need to calculate the approximate value of \(-\pi^2\).

  1. Calculate \(-\pi^2\): \[ \pi \approx 3.14 \quad \text{(noting that a more precise value is } 3.14159\text{)} \] Thus, \[ \pi^2 \approx 3.14 \times 3.14 \approx 9.8596 \] Therefore, \[ -\pi^2 \approx -9.8596 \]

  2. Value of \(-77\): \(-77\) is simply \(-77\).

Now we compare:

  • \(-\pi^2 \approx -9.86\)
  • \(-77\)

Since \(-9.86\) is greater than \(-77\), we find that:

\[ -\pi^2 > -77 \]

In conclusion, \(-77\) is less than \(-\pi^2\).

15/17 ? the square root of 3

To compare \(\frac{15}{17}\) and \(\sqrt{3}\), we can use approximate values.

  1. Calculate \(\frac{15}{17}\): \[ \frac{15}{17} \approx 0.8824 \]

  2. Calculate \(\sqrt{3}\): \[ \sqrt{3} \approx 1.732 \]

Now, we compare the two values:

  • \(\frac{15}{17} \approx 0.8824\)
  • \(\sqrt{3} \approx 1.732\)

Since \(0.8824 < 1.732\), we conclude that:

\[ \frac{15}{17} < \sqrt{3} \]

In conclusion, \(\sqrt{3}\) is greater than \(\frac{15}{17}\).

the square root of 159 ? 3pi

To compare \(\sqrt{159}\) and \(3\pi\), we need to calculate their approximate values.

  1. Calculate \(\sqrt{159}\): \[ \sqrt{159} \approx 12.593 \]

  2. Calculate \(3\pi\): Since \(\pi \approx 3.14159\), \[ 3\pi \approx 3 \times 3.14159 \approx 9.42477 \]

Now we compare the two values:

  • \(\sqrt{159} \approx 12.593\)
  • \(3\pi \approx 9.42477\)

Since \(12.593 > 9.42477\), we conclude that:

\[ \sqrt{159} > 3\pi \]

In conclusion, \(3\pi\) is less than \(\sqrt{159}\).