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Converting a number into scientific notation often starts with shifting the decimal point. The main goal of decimal shifts is to ensure that there is only one non-zero digit to the left of the decimal. In our example with the number 105.6, the decimal point is initially between 5 and 6.
Moving the decimal two places to the left, we get 1.056. This is now our coefficient for the scientific notation. The number of decimal shifts counts either as positive or negative. When shifting to the left, the exponent will be positive. When shifting to the right, the exponent will be negative. Counting these shifts helps in determining the correct exponent for the scientific notation, a crucial aspect to correctly represent the original number.

Scientific notation expresses a number as two parts: a coefficient and an exponent. The coefficient is the number derived after shifting the decimal point, ensuring it is between 1 and 10.
For 105.6, after shifting the decimal, the coefficient is 1.056. This part of the expression represents the simplified magnitude of the number. The exponent indicates how many times to multiply (or divide) the coefficient by 10 to get back to the original number. For positive exponents, it means you have shifted the decimal to the left to compact the size of the number. For negative exponents, the decimal is shifted to the right, expanding the number. In our example, the decimal shift was two places to the left, giving us an exponent of +2.
Thus, the number 105.6 is written as \(1.056 \times 10^2\) in scientific notation, where 1.056 is the coefficient, and 2 is the exponent.

The Power of 10 in scientific notation accounts for the amount and direction of decimal shifting. It is represented as \(10^n\) where \(n\) is the exponent.
This exponent reflects how many times, and in what direction, the original number's decimal was shifted to achieve the coefficient.When converting 105.6, the decimal shifted left by 2 places, so the exponent is +2.
Thus, the power of 10 for our example is \(10^2\), implying the original number is enlarged to reach 105.6 when \(1.056\) is multiplied by \(10^2\). Understanding the power of 10 allows you to quickly comprehend how large or small the number truly is, compared to its coefficient. This representation minimizes space and aids in easier calculations and comparisons of significantly larger or smaller numbers.