Question

Verifying an Answer
When Joanne checked her work by substituting the value of the variable back into the equation, she got an answer of 12.34 = 12.33. Explain why Joanne could have gotten the answer correct even though she did not get a true statement when she checked her work.

Answer 1

Most likely she used a rounded (approximate) value when she substituted. Small rounding errors can make two sides differ by a tiny amount even though the exact values are equal. For example, if the true value is 12.333... (37/3) and she rounded some intermediate result up to 12.34 but rounded the substituted value down to 12.33, her check would read 12.34 = 12.33 even though the exact values are equal. To avoid this, substitute the exact form (fractions or radicals) or keep more decimal places when checking.