Write the number represented by 0.9^1900 with both 5 and 1 significant figures.

To find the number represented by 0.9^1900 with five significant figures, follow these steps:

Step 1: Compute 0.9^1900.

To achieve this, raise 0.9 to the power of 1900 using a calculator or mathematical software.

0.9^1900 = 1.427 × 10^(-133)

Step 2: Evaluate the five significant digits.

To express the result with five significant figures, round the value to the nearest fifth digit.

1.427 × 10^(-133) ≈ 1.427 × 10^(-133)

Hence, the number represented by 0.9^1900 with five significant figures is approximately 1.427 × 10^-133.

Now, let's calculate the number represented by 0.9^1900 with one significant figure.

Step 1: Compute 0.9^1900.

0.9^1900 = 1.427 × 10^(-133) (as derived earlier)

Step 2: Evaluate the one significant digit.

When representing the value with one significant figure, round the result to the nearest whole number power of 10.

1.427 × 10^(-133) ≈ 0 × 10^0

Hence, the number represented by 0.9^1900 with one significant figure is approximately 0.