Final answer:
To remove decimals from an equation, you multiply or divide by powers of 10 to express numbers in scientific notation, adjust significant figures or decimal places, or balance a chemical equation with whole-number coefficients.
Step-by-step explanation:
When decimals are removed from an equation, particularly in a scientific context, the process is often related to the manipulation of significant figures, or when dealing with chemical equations, to ensure whole-number coefficients. Multiplying or dividing by powers of 10 is a standard method to eliminate decimals and express the numbers in scientific notation, which uses exponents to shift the decimal point.
For instance, multiplying 1.9436 by 102 will shift the decimal two places to the right, resulting in 194.36. Similarly, 2.4 x 10-2 will move the decimal two places to the left, giving 0.024.
To make chemical equations more readable and balance them with whole numbers, one might multiply all coefficients by a common factor. For example, if we have fractional coefficients in an equation, multiplying through by 2 might eliminate them. To maintain equality, the same operation must be applied to both sides of the equation.
There's also a rounding process to keep the correct number of significant figures or decimal places. For example, in addition and subtraction, the result should maintain the same number of decimal places as the least precise term, whereas in multiplication and division, the number of significant figures in the result should match the least precise term used in the operation.
Scientific notation is also used to express large or small numbers in a more compact form. This is done by shifting the decimal point to create a new number between 1 and 10, and then noting how many places the decimal moved as a power of ten.
For example, to express 965 in scientific notation, we'd write it as 9.65 x 102, indicating that the decimal has moved two places to the left. This method allows for easy multiplication and division as you add and subtract exponents, respectively.