divide 8.03 x 10^-8 and 1.95 x 10^6. show your work.
To divide \(8.03 \times 10^{-8}\) by \(1.95 \times 10^{6}\), we can use the quotient rule of exponents.
First, divide the two decimal numbers without considering the exponents:
\[ \frac{8.03}{1.95} \]
This gives us 4.12 as the result.
Next, consider the exponents. When dividing, subtract the exponent in the denominator from the exponent in the numerator and keep the same base (10):
\[ 10^{-8} - 10^{6} \]
To subtract the exponents, we subtract 6 from -8:
\[ -8 - 6 = -14 \]
Thus, the final result is \(4.12 \times 10^{-14}\).
To divide 8.03 x 10^-8 by 1.95 x 10^6, you can follow these steps:
Step 1: Divide the numerical values: 8.03 ÷ 1.95 = 4.12.
Step 2: Divide the exponents: 10^-8 ÷ 10^6 = 10^-8-6 = 10^-14.
Step 3: Combine the numerical result with the exponent result: 4.12 x 10^-14.
Therefore, 8.03 x 10^-8 divided by 1.95 x 10^6 equals 4.12 x 10^-14.
To divide numbers in scientific notation, we can divide the decimal parts and subtract the exponents.
Let's calculate the division of 8.03 x 10^-8 divided by 1.95 x 10^6 step by step:
Step 1: Divide the decimal parts
8.03 ÷ 1.95 ≈ 4.12
Step 2: Subtract the exponents
10^-8 / 10^6 = 10^(-8-6) = 10^-14
Therefore, 8.03 x 10^-8 divided by 1.95 x 10^6 is approximately 4.12 x 10^-14.
If you want to check the result using a calculator, you can enter the original numbers 8.03E-8 divided by 1.95E6 to get the answer in scientific notation, which should be 4.12E-14.