Real World Applications of Number Theory

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Real World Applications of Number Theory A. Rounding and Truncation 1. Student 1 received a score of 299 out of a possible 334 points for a term in an unknown class. To find what percentage the student received, one must take the score received and divide it by the total amount of points possible, and then multiply the quotient by 100. In this particular case, the teacher chose to use rounding to attain the final grade of the student. To round to the nearest whole number, one must consider the value in the tenths place. If the tenths place value is less than or equal to 4, the whole number stays the same and the rest of the decimal values are removed. If the tenths place is greater than or equal to 5, then the whole number is rounded up to the next possible whole number and the rest of the decimal values are removed. Therefore, the result of student 1’s final grade is a long decimal (89.520958), that when rounded to the nearest whole number properly, will produce 90% as a result, giving an A to student 1 for the term. 2. If the teacher chose to truncate to the nearest whole number for the final percentage of student 1, he/she would receive a B for their final grade. This is because when truncating to the nearest whole number, the decimal places are not considered and just removed without any sort of rounding, and the student will receive a 89% for the term. 3) Truncation of Income Tax Rate a) A taxpayer whose income tax rate is 27.8% might be happy to have truncation applied when it comes to filing taxes with the government. The reason for this is because when dealing with percentages, 27.8% literally means 27.8 cents is taken out of every dollar earned by this particular tax payer's income tax bracket and paid to the government; almost a quarter of the person's total earnings. So for example a person that made $40,000 dollars throughout the fiscal year would

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