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Significant figures are crucial when it comes to expressing numbers in scientific notation. These figures consist of all non-zero digits and any zeros that are embedded between them or following them in a decimal sequence. When dealing with a number like 72,400,000, only the non-zero digits (7 and 2) are considered as significant figures. Therefore, the significant figures in this scenario are discussed without explicitly counting trailing zeros, which are not considered significant unless after a decimal point.
To form a proper scientific notation, these significant figures are used to form the base of the expression. For 72,400,000, 7 and 2 combine to create 7.24 in the scientific notation format. Remember that the significant figures provide a way to express the precision of a number, which is particularly useful for very large or very small numbers.

The exponent in scientific notation is a key component that indicates the scale of the number. It informs us of how many places the decimal point has moved to convert a given number into a conveniently readable form. For example, with 72,400,000, determining the exponent involves counting the number of positions the decimal point shifts to place it directly after the first significant figure.

• For 72,400,000, the decimal point moves seven places to the left, resulting in an exponent of 7.
• This means in scientific notation form, you'll have a power of ten as part of the expression: \(10^7\).

Consequently, the full representation is \(7.24 \times 10^7\). This approach simplifies handling large numbers by focusing only on the magnitudes involved.

Non-zero digits play a crucial role in forming the backbone of scientific notation. These digits, which exclude any zeros that might be leading or trailing in the absence of a decimal, are the only numerics considered when forming the significant figure. In our example of 72,400,000, we identify the digits 7 and 2 as the non-zero digits.

These non-zero digits are always significant and must be used to express numbers accurately in scientific notation. By focusing on non-zero digits, we can effectively condense the information without losing its value. Therefore, non-zero digits help us focus on the actual numbers of importance, reducing the noise zeros add in very large or very small numbers.