Why should we clear decimals when solving linear equations and inequalities? Demonstrate how this is done with a solution.


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Oddman answered
Clearing decimals and fractions is a suggestion offered on the assumption that working with integers is easier than working with decimals or fractions. If you are confident in your ability to compute using decimals and fractions, it may make no difference in the speed or accuracy of your solution. Example   1.6x - 4.27 < 3   160x - 427 < 300    (multiply by 100 to clear decimals. The choice of 100 is determined by 4.27, which has a digit in the hundredths place.)   160x < 727    (add 427)   x < 727/160    (divide by x coefficient)   x < 4 87/160    (express as mixed number. This is the exact solution.)  Here's the same problem worked without clearing decimals. Note that fewer steps are needed, but the arithmetic is "more complicated" (if you're doing it without a calculator).   1.6x - 4.27 < 3   1.6x < 7.27    (add 4.27)   x < 7.27/1.6    (divide by the coefficient of x)   x < 4.54375    (this is the exact solution) _____ We could obtain the same (exact) solution by either method for this problem, because the coefficient of x is a number with factors that are powers of 2 and 5. If a number with other factors shows up in the denominator of the solution, the result may not be able to be expressed exactly as a decimal. (It might be an infinitely repeating decimal.) Of course, we could multiply 7.27/1.6 by 100/100 to get 727/160, as we had in the first solution.

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