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.