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Significant figures, also known as 'sig figs,' are crucial in scientific notation as they indicate the precision of a number. They include all the non-zero digits, any zeros between significant digits, and any trailing zeros in a decimal number.
For instance, in the number 8,750,000, the significant figures are 8.75, since trailing zeros without a decimal point are not considered significant in this context.
However, in 0.00000871, the significant figures are 8.71. The leading zeros are placeholders and do not count as significant.

Understanding significant figures is essential because they ensure that the representation of a number is as accurate as possible. In scientific notation, retaining the correct significant figures accurately portrays the value of the original number.

The 'powers of 10' concept is a fundamental part of scientific notation. It simplifies how large or small numbers are written and understood. The power of 10 indicates how many times you move the decimal point.
For example:

• In the number 8,750,000, you move the decimal point 6 places to the left, resulting in 8.75, hence it is written as \( 8.75 \times 10^6 \).
• Conversely, for a small number like 0.00000871, you move the decimal point 7 places to the right to get 8.71, hence it is expressed as \( 8.71 \times 10^{-7} \).

Each shift to the left multiplies the number by 10, and each shift to the right divides it by 10. This notation helps in simplifying and clearly representing very large or very small numbers.

The decimal point plays a crucial role in scientific notation. It helps in locating and transforming a number into a simpler form.
To convert a number to scientific notation, follow these steps:

• Identify the significant figures in the number.
• Determine where the decimal point needs to be placed so that there is only one non-zero digit to its left.
• Count the number of places the decimal point has been moved.

If the decimal point is moved to the left, the exponent will be positive, indicating how many times the number has been multiplied by 10.
If it's moved to the right, the exponent will be negative, indicating division by 10.
Understanding the placement and movement of the decimal point simplifies converting numbers and grasping their magnitude.