Scientific Notation Calculator

Step-by-step solution

1. 1

   Understand the input

   Read the input 0.00045. As an exact fraction it is 9/20000.

   $$0.00045 = \frac{9}{20000}$$
2. 2

   Find the exponent

   abs(v) = 0.00045. Since abs(v) is at least 10^-4 but below 10^-3, the exponent is -4.

   $$10^{-4} \le \lvert \frac{9}{20000} \rvert < 10^{-3}$$
3. 3

   Find the mantissa

   Divide the exact value by 10^-4: the mantissa is m = 9/2.

   $$\frac{\frac{9}{20000}}{10^{-4}} = 4.5$$
4. 4

   Result

   Scientific notation: 4.5 × 10^-4. Exact fraction: 9/20000. Standard form: 0.00045.

   $$0.00045 = 4.5 \times 10^{-4}$$
5. 5

   Check

   Check: multiplying the mantissa by 10^-4 expands back to the standard form 0.00045.

   $$4.5 \times 10^{-4} = 0.00045$$