Order from least to greatest:
`" "((3)/(5))/((8)/(10))" "(0.00751)/(0.01)" "(200)/(3)xx10^(-2)`

Answer

To order the given expressions from least to greatest, we will simplify each expression step by step.

### Step 1: Simplify the first expression \((3/5) / (8/10)\)

We can rewrite the division of fractions as multiplication by the reciprocal:

\[ \frac{3}{5} \div \frac{8}{10} = \frac{3}{5} \times \frac{10}{8} \]

Now, simplify the multiplication:

\[ = \frac{3 \times 10}{5 \times 8} = \frac{30}{40} \]

Now, simplify \(\frac{30}{40}\):

\[ = \frac{3}{4} = 0.75 \]

### Step 2: Simplify the second expression \((0.00751) / (0.01)\)

We can rewrite this division:

\[ \frac{0.00751}{0.01} = 0.00751 \div 0.01 \]

To simplify, we can multiply both the numerator and the denominator by 1000 to eliminate the decimal:

\[ = \frac{7.51}{10} = 0.751 \]

### Step 3: Simplify the third expression \((200/3) \times 10^{-2}\)

We can rewrite this expression as:

\[ \frac{200}{3} \times 10^{-2} = \frac{200}{3} \div 100 \]

This can be simplified to:

\[ = \frac{200}{300} = \frac{2}{3} \approx 0.6667 \]

### Step 4: Compare the values obtained

Now we have the following values:

1. First expression: \(0.75\)
2. Second expression: \(0.751\)
3. Third expression: \(0.6667\)

### Step 5: Order from least to greatest

Now we can order these values:

- \(0.6667\) (which corresponds to \(\frac{200}{3} \times 10^{-2}\))
- \(0.75\) (which corresponds to \((3/5) / (8/10)\))
- \(0.751\) (which corresponds to \((0.00751) / (0.01)\))

Thus, the order from least to greatest is:

\[ \frac{200}{3} \times 10^{-2} < \frac{3}{5} \div \frac{8}{10} < \frac{0.00751}{0.01} \]

### Final Answer

\[ \frac{200}{3} \times 10^{-2}, \frac{3}{5} \div \frac{8}{10}, \frac{0.00751}{0.01} \]

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