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8.03 x 10-8 ÷ 2.56 x 104

i need the exact answer

9 answers

To divide \( 8.03 \times 10^{-8} \) by \( 2.56 \times 10^{4} \), you can use the rules of dividing numbers in scientific notation:

  1. Divide the coefficients.
  2. Subtract the exponents.

Let's do the calculation step by step:

  1. Divide the coefficients: \[ \frac{8.03}{2.56} \approx 3.13515625 \]

  2. Subtract the exponents: \[ -8 - 4 = -12 \]

Now, combine the results: \[ 3.13515625 \times 10^{-12} \]

For simplicity, you can round the coefficient to a reasonable number of significant figures. If we round to three significant figures, we have: \[ 3.14 \times 10^{-12} \]

Thus, the exact answer in scientific notation is approximately: \[ 3.13515625 \times 10^{-12} \]

If you require rounding for significant figures, it would be: \[ 3.14 \times 10^{-12} \]

would it be a repeating fraction

The division of \( 8.03 \) by \( 2.56 \) yields a non-repeating decimal for practical purposes in scientific notation, which we calculated as approximately \( 3.13515625 \).

To clarify further, \( 3.13515625 \) is not a repeating decimal. It is a finite decimal number.

If you were to express this decimal as a fraction, it would also be a finite fraction and not a repeating one.

Thus, the result of the division \( 8.03 \times 10^{-8} \div 2.56 \times 10^{4} \) is best represented in scientific notation as \( 3.14 \times 10^{-12} \) (rounded to three significant figures), and the division does not yield a repeating fraction.

i need exact not approximate

To find the exact result of the division \( \frac{8.03 \times 10^{-8}}{2.56 \times 10^{4}} \) without rounding, let's proceed step by step.

Step 1: Divide the coefficients

Calculate the division of the coefficients:

\[ \frac{8.03}{2.56} \]

To perform the division:

\[ 8.03 \div 2.56 = 3.13515625 \]

Step 2: Subtract the exponents

Now subtract the exponents:

\[ -8 - 4 = -12 \]

Final Result

Combine the results:

\[ \frac{8.03 \times 10^{-8}}{2.56 \times 10^{4}} = 3.13515625 \times 10^{-12} \]

Conclusion

The exact result of the division is:

\[ 3.13515625 \times 10^{-12} \]

This is the exact answer in scientific notation.

can you write it in this layout
4/4=0

Certainly! Here’s the layout you're looking for:

\[ \frac{8.03 \times 10^{-8}}{2.56 \times 10^{4}} = 3.13515625 \times 10^{-12} \]

In this format, it clearly shows the division and the resulting value.

You're welcome! If you have any more questions or need further assistance, feel free to ask. Happy studying!