In 1995, the U.S. federal government paid off one-third of its debt. If the original amount of the debt eas $4,920,000,000,000, which expressions represents th amount that was not paid off?

Options

A. `1.64times10^(4)`
B. `1.64times10^(12)`
C. `3.28times10^(8)`
D. `3.28times10^(12)`

Answer

To solve the problem, we need to find the amount of debt that was not paid off after the U.S. federal government paid off one-third of its original debt.

**Step-by-step solution:**

1. **Identify the original debt amount:**
The original amount of the debt is given as $4,920,000,000,000, which can also be expressed in scientific notation as \( 4.92 \times 10^{12} \).

2. **Calculate one-third of the debt:**
To find out how much was paid off, we need to calculate one-third of the original debt:
\[ \text{Amount paid off} = \frac{1}{3} \times 4.92 \times 10^{12} \]
Performing the calculation:
\[ \text{Amount paid off} = 1.64 \times 10^{12} \]

3. **Determine the amount that was not paid off:**
Now, we subtract the amount that was paid off from the original debt to find the amount that was not paid off:
\[ \text{Amount not paid off} = 4.92 \times 10^{12} - 1.64 \times 10^{12} \]
Performing the subtraction:
\[ \text{Amount not paid off} = (4.92 - 1.64) \times 10^{12} = 3.28 \times 10^{12} \]

4. **Final expression:**
The expression that represents the amount that was not paid off is:
\[ 3.28 \times 10^{12} \]