The diameter of the sun is `(1.4 xx 10 ^(9))` m and the ditameter of the earth is `(1.2756 xx 10 ^(7))m.` Show that the diameter of the sun is nearly 100 times the diameter of the earth.

Answer

To show that the diameter of the sun is nearly 100 times the diameter of the earth, we can follow these steps:

### Step 1: Write down the diameters in scientific notation.
- Diameter of the sun = \(1.4 \times 10^9\) m
- Diameter of the earth = \(1.2756 \times 10^7\) m

### Step 2: Set up the division to find how many times the diameter of the earth fits into the diameter of the sun.
We need to calculate:
\[ \frac{\text{Diameter of the Sun}}{\text{Diameter of the Earth}} = \frac{1.4 \times 10^9}{1.2756 \times 10^7} \]

### Step 3: Simplify the expression.
We can separate the coefficients and the powers of ten:
\[ \frac{1.4}{1.2756} \times \frac{10^9}{10^7} \]
This simplifies to:
\[ \frac{1.4}{1.2756} \times 10^{9-7} = \frac{1.4}{1.2756} \times 10^2 \]

### Step 4: Calculate the coefficient.
Now, we need to calculate \(\frac{1.4}{1.2756}\):
\[ \frac{1.4}{1.2756} \approx 1.097 \]

### Step 5: Combine the results.
Now we can combine this with the power of ten:
\[ 1.097 \times 10^2 \approx 109.7 \]

### Step 6: Conclusion.
Since \(109.7\) is approximately \(100\), we can conclude that the diameter of the sun is nearly \(100\) times the diameter of the earth.

### Summary:
Thus, we have shown that:
\[ \text{Diameter of the Sun} \approx 100 \times \text{Diameter of the Earth} \]

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