Question

Put these numbers in order from least to greatest.

5.89(89 repeated) (the square root sign)4 5(pie symbol)

Answer 1

To compare the numbers given, let's first clarify and approximate each one:

1. **5.89(89 repeated)**: This is a repeating decimal. To convert it to a fraction, we can express it as \( x = 5.898989...\).
- Multiply by 100 (to shift two decimal places): \( 100x = 589.898989...\)
- Subtract the original equation from this:
\( 100x - x = 589.898989... - 5.898989... \)
\( 99x = 584 \)
\( x = \frac{584}{99} \approx 5.89899...\)

So, \( 5.89(89) \approx 5.899 \).

2. **\(\sqrt{4}\)**: The square root of 4 is \( 2 \).

3. **5π (5 times pi)**: The value of \(\pi\) is approximately \( 3.14\). Therefore:
\[
5\pi \approx 5 \times 3.14 \approx 15.7
\]

Now, let's put these together for comparison:

- \( 5.89(89) \approx 5.899 \)
- \( \sqrt{4} = 2 \)
- \( 5\pi \approx 15.7 \)

Now, we order them from least to greatest:

1. \( \sqrt{4} = 2 \)
2. \( 5.89(89) \approx 5.899 \)
3. \( 5\pi \approx 15.7 \)

So, the final order from least to greatest is:

\[
\sqrt{4}, \: 5.89(89), \: 5\pi
\]