Put these numbers in order from least to greatest:
a. `234xx10^(-2)`
b. `0.234xx10^(2)`
c. `2.34xx10^(4)`

Answer

To put the numbers in order from least to greatest, we need to evaluate each number. Let's break it down step by step.

### Step 1: Evaluate the first number
The first number is \( 234 \times 10^{-2} \).

To evaluate this, we can rewrite it as:
\[ 234 \times 10^{-2} = 234 \times \frac{1}{10^2} = 234 \times \frac{1}{100} = \frac{234}{100} = 2.34 \]

### Step 2: Evaluate the second number
The second number is \( 0.234 \times 10^{2} \).

To evaluate this, we can shift the decimal point to the right by 2 places:
\[ 0.234 \times 10^{2} = 0.234 \times 100 = 23.4 \]

### Step 3: Evaluate the third number
The third number is \( 2.34 \times 10^{4} \).

Again, we shift the decimal point to the right by 4 places:
\[ 2.34 \times 10^{4} = 2.34 \times 10000 = 23400 \]

### Step 4: Compare the evaluated numbers
Now we have:
- \( a = 2.34 \)
- \( b = 23.4 \)
- \( c = 23400 \)

### Step 5: Order the numbers from least to greatest
Now we can order these numbers:
- The smallest number is \( a = 2.34 \)
- The next is \( b = 23.4 \)
- The largest is \( c = 23400 \)

Thus, the order from least to greatest is:
\[ a < b < c \quad \text{or} \quad 2.34 < 23.4 < 23400 \]

### Final Answer
The numbers in order from least to greatest are:
\[ 234 \times 10^{-2}, \quad 0.234 \times 10^{2}, \quad 2.34 \times 10^{4} \]

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