Converting from Scientific to Standard Notation

Sure, let's go through the steps to convert a number from scientific notation to standard notation.

1. Identify the components of the scientific notation: Scientific notation is typically written in the form $a \times 10^n$, where $a$ is a number greater than or equal to 1 and less than 10, and $n$ is an integer.

2. Determine the value of $a$: This is the coefficient in the scientific notation.

3. Determine the value of $n$: This is the exponent in the scientific notation.

4. Move the decimal point:

   • If $n$ is positive, move the decimal point in $a$ to the right $n$ places.
   • If $n$ is negative, move the decimal point in $a$ to the left $n$ places.

5. Fill in with zeros if necessary: If moving the decimal point creates empty places, fill them with zeros.

Let's go through an example:

Example: Convert $3.45 \times 10^4$ to standard notation

1. Identify the components: $a = 3.45$ and $n = 4$.

2. Move the decimal point: Since $n$ is 4, move the decimal point in $3.45$ four places to the right.

   • 3.45 → 34.5 → 345 → 3450 → 34500

3. Result: The standard notation is 34500.

Example: Convert $6.78 \times 10^{-3}$ to standard notation

1. Identify the components: $a = 6.78$ and $n = -3$.

2. Move the decimal point: Since $n$ is -3, move the decimal point in $6.78$ three places to the left.

   • 6.78 → 0.678 → 0.0678 → 0.00678

3. Result: The standard notation is 0.00678.

By following these steps, you can convert any number from scientific notation to standard notation.