To find out how many times smaller \( 2.7 \times 10^3 \) is than \( 5.481 \times 10^5 \), we can divide the two numbers.
First, we calculate:
\[ \frac{2.7 \times 10^3}{5.481 \times 10^5} \]
This can be simplified to:
\[ \frac{2.7}{5.481} \times \frac{10^3}{10^5} \]
Now we simplify \( \frac{10^3}{10^5} \):
\[ \frac{10^3}{10^5} = 10^{3-5} = 10^{-2} = 0.01 \]
Next, we need to calculate \( \frac{2.7}{5.481} \):
\[ \frac{2.7}{5.481} \approx 0.4928 \quad \text{(approximately)} \]
Now, multiplying this value by \( 0.01 \):
\[ 0.4928 \times 0.01 = 0.004928 \]
To find out how many times smaller it is, we can also calculate the inverse:
To express how many times smaller \( 2.7 \times 10^3 \) is than \( 5.481 \times 10^5 \):
\[ \text{Number of times smaller} = \frac{5.481 \times 10^5}{2.7 \times 10^3} \]
This will result in:
\[ = \frac{5.481}{2.7} \times \frac{10^5}{10^3} \]
Simplifying \( \frac{10^5}{10^3} \):
\[ = \frac{5.481}{2.7} \times 10^{5-3} = \frac{5.481}{2.7} \times 10^2 \]
Calculating \( \frac{5.481}{2.7} \):
\[ \frac{5.481}{2.7} \approx 2.03 \quad \text{(approximately)} \]
Thus, we multiply by \( 10^2 \):
\[ 2.03 \times 100 = 203 \]
So, \( 2.7 \times 10^3 \) is approximately 203 times smaller than \( 5.481 \times 10^5 \).
Therefore, the answer is:
203