Name: Jim Handy
Student ID: #########
Assessment: HHT Task 1 Part A

Part A: Rounding and Truncation
Determine if the student should receive an A letter grade if the student received 299 points of 334 possible. We could think of this as a basic division question, or we could think of it as the fraction:

[pic]

A1: The teacher will likely give this student an A letter grade since percentages are typically represented as a whole number and it is generally accepted that we round up when the tenths value is five or greater (Blitzer, 2006); so the teacher will consider this a 90%.

A2: If the teacher were to truncate the percentage to just the hundredths place, then the student would not receive an A letter grade because the grade would be simply be considered: 89%

A3: Tax Payment

As previously demonstrated, applying rounding and truncation can have a dramatic effect on the end result. To further illustrate the impact of rounding and truncation on an individual’s bottom line let’s pretend that the United States government were to tax you at a rate of 27.8%. What this means is that that for every $1 dollar earned, you would be expected to pay 27.8 cents to the Internal Revenue Service. Since private citizens do not have anything smaller than a penny to pay their taxes and there are heavy penalties for underpayment, IRS tax forms require whole dollar amounts using the same rounding principals applied to the student’s grade in part A1, where partial dollar amounts above 0.50 cents are rounded to the next whole dollar (IRS 2011).

We can see easily see from the following graph why the taxpayer would prefer to truncate their tax rate as truncation saves them nearly a full percent in taxes which equates to 8 to 10 dollars for every $1,000 earned.

[pic]

A3 Part B Examples:

|Truncation |Dinner Plans |
| |Truncation is very useful when calculating something where the penalty for coming up short is embarrassing or |
| |uncomfortable. For instance, let’s pretend we’re serving pizza to eight friends and that the box claims that each |
| |small pizza will serve approximately 2.5 adults. |
| | |
| |If we were to take to take the box for its word we might need a bit of help calculating out how many pizzas to buy: |
| |[pic] |
| | |
| |Since we have no way of purchasing 1/5th of a pizza, and we don’t want anyone to go hungry, we’ll truncate the 0.5 |
| |serving from each pizza. |
| | |
| |[pic] |
| | |
| |Not only does this make calculating the number of pizzas to purchase easier, but it also means that more than likely |
| |we’ll either have just enough or a little more pizza left over. |
| |Fuel Consumption |
| |Another time truncating comes in very handy is when preparing for a trip in the car. If you know that your car gets |
| |approximately 16.5 miles per gallon and you have a 100 mile trip to take, you could go so far to estimate that at 16.5 |
| |miles per gallon, you would need |
| |[pic] |
| | |
| |Since so many variables affect a vehicle’s fuel economy, we’ll truncate the previous average to 16 miles per gallon and|
| |estimate that it will take a little more gas; worse case in this situation is that we have a bit more to get home with.|
| | |
| |[pic] |
|Rounding |Estimating Retail Discounts |
| |In a buying frenzy, it’s sometimes difficult to figure out exactly how much something is when the store is offering a |
| |certain percentage off. Rounding permits us to quickly approximate the amount of a discount we’ll receive by |
| |simplifying our calculations. Let’s take the following sale items for example: |
| | |
| | |
| |Percentage |
| |Actual Price |
| |Discount |
| | |
| | |
| |Percentage |
| |Rounded Price |
| |Discount |
| | |
| |Hammer |
| |10.00% |
| |$13.47 |
| |$1.35 |
| | |
| |Hammer |
| |10.00% |
| |$13.00 |
| |$1.30 |
| | |
| |Drill |
| |10.00% |
| |$19.50 |
| |$1.95 |
| | |
| |Drill |
| |10.00% |
| |$20.00 |
| |$2.00 |
| | |
| |Saw |
| |15.00% |
| |$22.25 |
| |$3.34 |
| | |
| |Saw |
| |15.00% |
| |$22.00 |
| |$3.30 |
| | |
| | |
| | |
| | |
| |$6.63 |
| | |
| | |
| | |
| | |
| |$6.60 |
| | |
| |As you can see, we simplified our calculations by rounding to the nearest whole dollar and came up within pennies of |
| |the actual discount. |
| |Estimating Monthly Expenses |
| |A key to maintaining a healthy credit score in this economy is staying on top of your monthly expenses by closely |
| |adhering to a budget. Since there’s rarely a shortage of a ways to spend excess money, rounding your typical monthly |
| |expenses can be a handy method of staying on track. Let’s use the following table as an example: |
| | |
| | |
| |Actual Expense Estimate |
| | |
| | |
| | |
| | |
| |January |
| |February |
| |March |
| |April |
| |Average |
| |Rounded |
| | |
| |Housing |
| |$500.00 |
| |$500.00 |
| |$500.00 |
| |$500.00 |
| |$500.00 |
| |$500.00 |
| | |
| |Electric |
| |$152.33 |
| |$162.13 |
| |$158.49 |
| |$159.74 |
| |$158.17 |
| |$160.00 |
| | |
| |Gas |
| |$47.88 |
| |$47.24 |
| |$43.23 |
| |$42.12 |
| |$45.12 |
| |$50.00 |
| | |
| |Water |
| |$12.86 |
| |$13.28 |
| |$12.99 |
| |$10.99 |
| |$12.53 |
| |$10.00 |
| | |
| |Groceries |
| |$163.22 |
| |$160.92 |
| |$172.48 |
| |$142.76 |
| |$159.85 |
| |$160.00 |
| | |
| |Internet |
| |$40.99 |
| |$40.99 |
| |$40.99 |
| |$40.99 |
| |$40.99 |
| |$40.00 |
| | |
| | |
| |$917.28 |
| |$924.56 |
| |$928.18 |
| |$896.60 |
| |$916.66 |
| |$920.00 |
| | |
| | |
| |Tracking our actual monthly expenses from January to April, has allowed us to come up with our monthly average for of |
| |our “necessities”. |
| | |
| |Since it would impractical keep track of or discuss with neighbors the cost of your electricity or grocery bill in |
| |anything less than tens, we round each of necessity to the nearest ten place and from this come up with a monthly |
| |budget. |
| | |
| |Even though rounding will occasionally have a similar effect to truncating (as in the Internet expense) in general, you|
| |should find that you’ll see come out ahead in most months. |

Reference List

Blitzer, Robert. (2006). Thinking Mathematically, 4e. (pp. 13-14) Retrieved from CourseCompass.com

U.S., Department of Treasury (2011). Tax Guide 2011 (pp. 12) Retrieved from http://www.irs.gov/pub/irs-pdf/p17.pdf