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Scientific notation is a way of expressing numbers that are too large or too small in a compact form. When converting a number to scientific notation, the goal is to rewrite the number so that it is between 1 and 10 multiplied by a power of 10.

For example, taking the number 0.00086, we start by finding the non-zero digit furthest to the left, which is 8. We then move the decimal point to the right of that digit to form a new number between 1 and 10, in this case, 8.6. Counting the number of places we moved the decimal, which is four, gives us the exponent for the power of 10. Since we moved the decimal to the right, the exponent will be negative, conveying that the original number is less than one. Thus, by following these steps, we can convert 0.00086 to scientific notation as \(8.6 \times 10^{-4}\).

Exponents play a crucial role in scientific notation as they indicate the scale of the number. Understanding how to determine and apply the exponent is essential.

If you move the decimal to the right to create a number between 1 and 10, as in our previous example with 0.00086, the exponent on the 10 will be negative. This signifies division by a power of ten (making the number smaller). Conversely, if you move the decimal to the left, the exponent will be positive, reflecting multiplication by a power of ten (making the number larger). The exponent indicates exactly how many places the decimal has moved. Remember, the base is always 10, which simplifies multiplication and division because moving the decimal is a visual representation of these operations.

Significant figures are the digits in a number that carry meaning towards its precision. When converting to scientific notation, it's important to retain all of the original significant figures from the given number.

In our given number, 0.00086, there are two significant figures: 8 and 6. Zeros to the left of the first non-zero digit are not considered significant as they only indicate the position of the decimal point. Retaining the significant figures is crucial when expressing the number in scientific notation because it maintains the precision of the original measurement. Thus, when we write \(8.6 \times 10^{-4}\), we maintain both significant figures from the original number, reflecting its precision accurately.