Question

Put these numbers in order from least to greatest:
1) −6.63324958 (-44)
2) 2.625 (21/8)
3) 4.2 (4 1/5)
4) −4.7¯(-43/9)

Answer 1

To order the numbers from least to greatest, let's first clarify what each number is and convert them to comparable forms:

1) **−6.63324958** (approximately -6.63324958)
2) **2.625** (which is \( \frac{21}{8} \))
3) **4.2** (which is \( 4 \frac{1}{5} = 4.2 \))
4) **−4.7¯** (the notation suggests that it's a repeating decimal representing \(-\frac{43}{9}\)).

We will convert **−4.7¯** to a decimal. The repeating decimal \(-4.7\) with an overline indicates that only the digit **7** repeats. This can be represented as follows:

\[
x = -4.77777\ldots
\]

To express it as a fraction:
1. Set \( x = -4.7\overline{7} \).
2. Multiply both sides by 10 to shift the decimal: \( 10x = -47.77777\ldots \).
3. Now subtract \( x \) from \( 10x \):

\[
10x - x = -47.77777\ldots + 4.77777\ldots
\]
\[
9x = -43
\]
\[
x = -\frac{43}{9} \approx -4.77777\ldots
\]

Now we have the following approximate values for comparison:
1) **−6.63324958**
2) **2.625**
3) **4.2**
4) **−4.77777...**

Now we can list these numbers in order from least to greatest:

- **−6.63324958**
- **−4.77777...**
- **2.625**
- **4.2**

Thus, the final order from least to greatest is:

1) −6.63324958
4) −4.7¯
2) 2.625
3) 4.2