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Understanding significant figures is crucial in scientific notation. Significant figures refer to the digits in a number that contribute to its precision. Any non-zero digit is a significant figure. Zeroes can be tricky - they may or may not be significant depending on their position.

In the number 45,000, the non-zero digits are 4 and 5. These are our significant figures because they define the value of the number with precision. All the trailing zeros in this particular number are not significant because they only indicate the scale or magnitude of the number, not its precision.

When converting to scientific notation, always start by identifying these critical digits. This ensures the number's precision is preserved while also making it easier to handle large numbers.

The placement of the decimal point is a vital step in scientific notation. Scientific notation requires placing the decimal point after the first significant figure.

For our example, 45,000, we identify 4 as the first significant figure. We then place the decimal point immediately after it, resulting in 4.5. This step normalizes the number, meaning it falls within the range of 1 and 10, making it easier to use in calculations.

It's important to note that the movement of the decimal point will dictate the exponent's value. In moving the decimal point from its original position at the end of 45,000 (after the last zero) to its new position (after the 4), we count the amount of places it moved to the left, which is 4 in this case.

Exponents in scientific notation indicate how many places the decimal point was moved. This value is written as a power of 10.

If the original decimal point was moved to the left, as in our example 45,000, the exponent will be positive. Conversely, if the decimal point moves to the right, the exponent will be negative.

In our example, the decimal point in 45,000 is moved 4 places to the left to reposition it after the 4, resulting in the number 4.5. Hence, the exponent is 4. Therefore, in scientific notation, 45,000 is written as \( 4.5 \times 10^4 \).

By converting to scientific notation, large numbers become more manageable and easier to read, eliminating a string of zeros that can be cumbersome and error-prone in calculations.