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Decimal movement is an essential part of converting a number into scientific notation. To move the decimal point, count how many places you need to shift it so that only one non-zero digit is to the left of the decimal point. For example, with 0.00203, the decimal moves 3 places to the right to become 2.03.

This shift determines the power of 10 in the final scientific notation. If you move the decimal to the right, the power of 10 will be negative. Conversely, if you move it to the left, the power will be positive. In our example, we've moved the decimal 3 places to the right, so the power is -3.

This step transforms the original number into a convenient and standardized form which is highly useful in mathematical and scientific calculations.

Significant digits are the digits in a number that carry meaning and contribute to its precision. In scientific notation, these are the digits that you write before the multiplication sign and the power of 10. For example, in the number 0.00203, the significant digits are 2.03.

Understanding which digits are significant is crucial, as it directly affects the accuracy of your scientific notation. Zeroes that are placeholders do not count as significant digits, whereas zeroes between non-zero digits or following them do. In 0.00203, the three leading zeros are not significant, but the two zeroes between 2 and 3 are significant because they contribute to the value of the number.

When writing a number in scientific notation, always ensure to only include the significant digits, as they represent the true precision of the number.

In scientific notation, the power of 10 indicates how many times the decimal point has been moved to convert the original number into its more compact form. This exponent tells us whether we moved the decimal point to the right or the left and how many places it was moved.

For the number 0.00203, we move the decimal point 3 places to the right to get 2.03. Therefore, the power of 10 is -3, and we write the number as \[2.03 \times 10^{-3}\].

The power of 10 is a powerful concept because it allows us to express very large or very small numbers in a convenient and readable form. This approach is extensively used in science and engineering to deal with magnitudes that span a wide range without the practical limitations of written form.