(a) Write the numbers $$ 0.017,0.007,0.01 \overline{7}, 0.027 $$ in order from least to greatest. $$ \square
abla \square $$

Question

(a) Write the numbers $$ 0.017,0.007,0.01 \overline{7}, 0.027 $$ in order from least to greatest. $$ \square 
abla \square $$

UpStudy AI · Accepted Answer

To compare the numbers $$ 0.017, 0.007, 0.01 \overline{7}, 0.027 $$, we will first convert $$ 0.01 \overline{7} $$ into a fraction for easier comparison.

1. **Convert $$ 0.01 \overline{7} $$ to a fraction:**
   Let $$ x = 0.01 \overline{7} $$.
   Then, $$ 100x = 1.7 \overline{7} $$.
   Subtracting the first equation from the second gives:
   $$
   100x - x = 1.7 \overline{7} - 0.01 \overline{7}
   $$
   $$
   99x = 1.69
   $$
   $$
   x = \frac{1.69}{99}
   $$
   To convert $$ 1.69 $$ to a fraction:
   $$
   1.69 = \frac{169}{100}
   $$
   Thus,
   $$
   x = \frac{169}{100 \times 99} = \frac{169}{9900}
   $$

2. **Convert all numbers to decimals for comparison:**
   - $$ 0.007 $$ is already in decimal form.
   - $$ 0.017 $$ is already in decimal form.
   - $$ 0.01 \overline{7} $$ is approximately $$ 0.017 $$ (as calculated).
   - $$ 0.027 $$ is already in decimal form.

3. **List the numbers:**
   - $$ 0.007 $$
   - $$ 0.017 $$
   - $$ 0.01 \overline{7} \approx 0.017 $$
   - $$ 0.027 $$

4. **Order from least to greatest:**
   - $$ 0.007 $$
   - $$ 0.017 $$
   - $$ 0.01 \overline{7} $$
   - $$ 0.027 $$

Thus, the final order from least to greatest is:
$$
0.007, 0.017, 0.01 \overline{7}, 0.027
$$
The numbers ordered from least to greatest are $$ 0.007, 0.017, 0.01\overline{7}, 0.027 $$.

(a) Write the numbers \( 0.017,0.007,0.01 \overline{7}, 0.027 \) in order from least to greatest. \( \square \nabla \square \)

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