Convert the following numbers to scientific notation: a. 7,000,000,000 b. 0.00346 c. 1,238

When dealing with large numbers, scientific notation comes in handy to make these values easier to read and work with. For example, converting the number 7,000,000,000 into scientific notation helps reduce the clutter of zeros. You start by identifying the first non-zero digit, which in this case is 7, and then place a decimal point after it to get 7.0.
Next, you count the number of places from the decimal point to the end of the number, which is 9 in this instance. Therefore, 7,000,000,000 is written as:
\(7 \times 10^{9}\)
This tells us that the original large number can be represented concisely and still convey the same value.
*When working with large numbers*, always remember:

• Identify the first non-zero digit.
• Place the decimal point after this digit.
• Count the number of digits to the right of the decimal point.

Small numbers, especially those less than one, can also be simplified using scientific notation. By doing so, we express these values in a more compact format, removing unnecessary leading zeros. Take 0.00346 as an example. To convert this number, start by identifying the first non-zero number, which is 3.46.
Place a decimal point right after it. Now, count the number of places the decimal point moved from its original position; in this case, it’s 3 places to the right. Hence, 0.00346 in scientific notation is:
\(3.46 \times 10^{-3}\)
This notation helps streamline calculations and provides clarity.
*When dealing with small numbers, follow these steps*:

• Identify the first non-zero digit.
• Place the decimal point directly after this digit.
• Count the number of decimal places the point was moved to reach its current position.

Place value is crucial when converting to scientific notation because it assists in determining the power of 10. For any number, the position of a digit impacts its value. For example, the great difference in value between 1,238 and 1238 stems from their place values.
Let's consider converting 1,238 to scientific notation. Start by recognizing the first digit (1) and place a decimal after it, forming 1.238. Then, count how many places you moved the decimal point, which in this case is 3. So, 1,238 becomes:
\(1.238 \times 10^{3}\)
This notation allows you to see that 1.238, when scaled by \(10^3\), represents 1,238.
*When using place value for scientific notation, keep in mind*:

• The position of each digit determines its multiplier.
• Right of the decimal increases values by powers of 10 (large numbers).
• Left of the decimal decreases values by negative powers of 10 (small numbers).