Percents

= = = Percents: percent - (%) means "Parts of 100". = = A percent is a ratio whose second term is 100. Percent means parts per hundred and we use the symbol % to represent it. = = = = Example: = = 19% - 19 of 100 = = 19 parts can be expressed as the ratio 19/100. One percent can be expressed as 1 part to 100, or 1/100. Thus, 1% is 1/100 or 0.01 = = = = To write a percent as a fraction, remove the percentage sign and multiply by 1/100. = = Example: = = 67% = 67 x (1/100) = 67/100 = = = To write percent as a decimal, remove the percent sign % and multiply by 0.01 = = Example: = = 19% = 19 x (0.01) = 0.19 = [ remove the % sign and move the decimal point two places to the left ] = = = = Examples: = = 150% = 150 x (1/100) = 150/100 = 150% = 150 x (0.01) = 1.50 = = = 66 2/3 = 66 2/3 x (1/100) = = 200/3 x (1/100) = 200/300 = 2/3 = = = 0.35 = 0.35 x (0.01) = 0.0035

= Fractions and Decimals as Percents - % = =A fraction or decimal can be written as a percent by multiplying 100 %.= **Multplying by 100 is the same as multiplying by 1. 100% is 100/100 or 1**

Fraction - 7/8 = 7/8 x (100%) = 700/8 = 87.5% Decimal - 0.64 = 0.64 x (100%) = 64%
 * Examples:

Fraction - 3/11 = 3/11 x (100%) = 300/11 % = 27 3/11 % Decimal - 1.78 = 1.7 x (100%) = 178%**

= Engine Cylinder Balance and Percent Change - Automotive =
 * 

Cylinder Balance Worksheet 1: Vocabulary **


 * 1. Percent – parts per 100.

2. Percent Change – the difference between two numbers divided by the original number, then multiplied by 100 to change to a percent.**

Percent Decrease and Percent Increase may all be used in conjunction with Percent Change.
 * 3. Percent Drop, Percent Rise, Percent Mark-Down, Percent Mark-Up,

4. RPM – revolution per minute of an engine.

5. Cylinder – the part of an engine where combustion is taking place.

6. Cylinder Disabled – Disabling a cylinder so that combustion will not take place.**


 * Engine Cylinder Balance Worksheet #2: Checking for Understanding **


 * 1) **When doing a cylinder balance test on a 8-cylinder engine you come up with the following results:**


 * **Cylinder ** || **RPM drop from 825 to** ||
 * **1 ** || **712 ** ||
 * **2 ** || **715 ** ||
 * **3 ** || **720 ** ||
 * **4 ** || **684 ** ||
 * **5 ** || **700 ** ||
 * **<span style="font-family: 'Arial','sans-serif';">6 ** || **<span style="font-family: 'Arial','sans-serif';">730 ** ||
 * **<span style="font-family: 'Arial','sans-serif';">7 ** || **<span style="font-family: 'Arial','sans-serif';">725 ** ||
 * **<span style="font-family: 'Arial','sans-serif';">8 ** || **<span style="font-family: 'Arial','sans-serif';">695 ** ||


 * The manufacturer requires a least a 12% drop in RPM’S when a cylinder is disabled. Complete the following chart. (Round to the nearest tenth of a percent)**

(Original – Final) ** || **__<span style="font-family: 'Arial','sans-serif';">(Original – Final) __ <span style="font-family: 'Arial','sans-serif';">Original ** || **<span style="font-family: 'Arial','sans-serif';">Multiply by 100 ** || <span style="font-family: 'Arial','sans-serif';"> = = <span style="color: #008000; display: block; font-family: 'Arial','sans-serif'; font-size: 14pt; text-align: left;">**Cost Estimation Worksheet #1** Formula Information__:__ ** t = Total Time in Hours mn = Material Cost per part qn = Quantity of part s = Sales tax rate in percent subtotal = (l • t) + (m1 • q1) + (m2 • q2) + … + (mn • qn) total cost = subtotal + (s • subtotal) **
 * **<span style="font-family: 'Arial','sans-serif';">Cylinder ** || **<span style="font-family: 'Arial','sans-serif';">RPM 825 TO ** || **<span style="font-family: 'Arial','sans-serif';">Total RPM drop
 * **<span style="font-family: 'Arial','sans-serif';">1 ** ||  ||   ||   ||   ||
 * **<span style="font-family: 'Arial','sans-serif';">2 ** ||  ||   ||   ||   ||
 * **<span style="font-family: 'Arial','sans-serif';">3 ** ||  ||   ||   ||   ||
 * **<span style="font-family: 'Arial','sans-serif';">4 ** ||  ||   ||   ||   ||
 * **<span style="font-family: 'Arial','sans-serif';">5 ** ||  ||   ||   ||   ||
 * **<span style="font-family: 'Arial','sans-serif';">6 ** ||  ||   ||   ||   ||
 * **<span style="font-family: 'Arial','sans-serif';">7 ** ||  ||   ||   ||   ||
 * **<span style="font-family: 'Arial','sans-serif';">8 ** ||  ||   ||   ||   ||
 * According to your calculations in the above chart, which cylinder is not producing power? Explain your answer.**
 * Name: __Session:__ Date:
 * <span style="color: #000000; font-family: 'Arial','sans-serif';">l = Labor Cost

<span style="color: #000000; font-family: 'Arial','sans-serif'; font-size: 12pt; font-weight: normal;">**1. What is the total cost of a job, if the flat rate time is 0.2 hours, the hourly rate is $45.00 and the cost of materials is $2.50 (only one is needed)? The tax rate is 6%.

2. Sam estimates that it will take him 0.6 hours to do an oil change. The cost of the filter is $7.95, and oil is $1.70/qt. If a vehicle takes 5 quarts and his flat rate is $35.00/hr, how much will it cost for the oil change?**


 * 3. Replacing a water pump on a 2008 Toyota Camry takes 2.3 hours to complete. The shop rate is $48.00/hr, the water pump cost $34.50, and it requires 2 gallons of anti-freeze at $6.50/gallon. Sales tax rate is 7%. What is the total cost of the job?

4. Given the formula A = (b1 + b2) /2 • h. Find A if b1 = 12 b2 = 18 h = 5**

**<span style="color: #ff0000; font-family: 'Arial','sans-serif'; font-size: 14pt;">__Cost Estimation Worksheet #1 Key__ **

(45 • 0.2) + 2.50 9 + 2.50 = 11.50
 * <span style="font-family: 'Arial','sans-serif';">1. Subtotal = (l • t) + m

Total Cost = Subtotal + (s • Subtotal) 11.50 + (6% • 11.50) = $12.19

2. (35 • 0.6) + (7.95) + (1.7 • 5) 21.00 + 7.95 + 8.50 = $37.45 Subtotal & Cost

3. (48 • 2.3) + (34.50) + (6.50 • 2) 110.40 + 34.50 + 13.00 = $168.95 Total Cost

4. A=(12 + 18)/2 • 5 ** <span style="display: block; font-family: 'Arial','sans-serif'; text-align: left;">**A=75**

<span style="color: #ff00ff; display: block; font-family: 'Arial','sans-serif'; font-size: 14pt; text-align: left;">**__Engine Cylinder Balance Worksheet #3: Applying the Concept__** =<span style="color: #000000; font-family: 'Arial','sans-serif';">Show all work below each problem. =

<span style="color: #000000; font-family: 'Arial','sans-serif';">**1. Prior to tuning up a 1998 Geo Metro, you test it on a dyno and find its horsepower to be 49 hp. After tuning it up you test it again and find its horsepower to be 53 hp. What is the percent change (Percent Rise in horsepower) based on the horsepower before the tune-up?**


 * 2. If the temperature changes from 64 degrees to 72 degrees, what is the percent increase in temperature__?__**


 * 3. A sales manager wants to mark down the price of a pair of jeans from $32.50 to $26.00. What percent mark-down should be listed on the sale sign?**


 * 4. A set of JVC speakers cost $280.00 in January. By December the price had increased to $322.00. What was the percent mark-up of the speakers__?__

5. A gallon of gas cost $1.50 in 2004. In 1980 a gallon of gas cost $0.90. If you go back to 1980, what is the percent decrease in a gallon of gasoline from now until then?

6. You have performed very well on your new job. Without even requesting it your boss gave you a $2.50 raise. If your previous wage was $6.25, what was the percent increase__ of your raise?**

<span style="color: #00ff00; display: block; font-family: 'Arial','sans-serif'; font-size: 14pt; text-align: center;">** Cylinder Balance Worksheet #3 Key **

<span style="font-family: 'Arial','sans-serif';">**1. 53 - 49 = 4**
 * 4/49 = 8.1%**


 * 2. 72 – 64 = 8**
 * 8/64 = 12.5%**


 * 3. 32.50-26=6.50**
 * 6.50/32.50 = 20%**


 * 4. 322 – 280 = 42**
 * 42/280 = 15%**


 * 5. 1.50 - 0.90 = 0.60**
 * .60/1.50 = 40%**


 * 6. 6.25 + 2.50 = 8.75**


 * 2.50/6.25 = 40%**

**We use the percent symbol (%) to express percent. Percents are used everywhere in real life, so you'll need to understand them well. Here are three ways to write the same thing:** <span style="font-family: 'Verdana','sans-serif'; font-size: 10pt;">
 * 15% = 15/100 = 0.15**

Fifteen percent is the same as the fraction 15/100 and the decimal 0.15. They all simply mean "fifteen out of a hundred." A percent can always be written as a decimal, and a decimal can be written as a percent, like this: <span style="font-family: 'Verdana','sans-serif'; font-size: 10pt;">0.85 = 85% <span style="font-family: 'Verdana','sans-serif'; font-size: 10pt;">We can find any percent of a given number by changing the percent to a decimal and multiplying. One hundred percent of a number is just the number itself. Two hundred percent of a number is twice that number. <span style="font-family: 'Verdana','sans-serif'; font-size: 10pt;">100% of 50 -> 50 200% of 50 -> 2 x 50 = 100 <span style="font-family: 'Verdana','sans-serif'; font-size: 10pt;">Let's find 30 percent of 400: First change 30% to a decimal by moving the decimal point 2 places to the left. <span style="font-family: 'Verdana','sans-serif'; font-size: 10pt;">30% = 0.30 <span style="font-family: 'Verdana','sans-serif'; font-size: 10pt;">Then multiply. <span style="font-family: 'Verdana','sans-serif'; font-size: 10pt;">0.30 x 400 = 120 <span style="font-family: 'Times New Roman','serif'; font-size: 10pt;">30% of 400 is 120.
 * //<span style="font-family: 'Verdana','sans-serif'; font-size: 10pt;">

Mental Math Hint: //** <span style="font-family: 'Verdana','sans-serif'; font-size: 10pt;">There's an easy way to find 10% of a number without multiplying. Just move the decimal point in the number left by one place. Let's try it with these numbers: <span style="font-family: 'Verdana','sans-serif'; font-size: 10pt;">895 27 10,411 10% of 895 = 89.5 10% of 27 = 2.7 10% of 10,411 = 1,041.1 <span style="font-family: 'Verdana','sans-serif'; font-size: 10pt;">Write each as a percent: <span style="font-family: 'Verdana','sans-serif'; font-size: 10pt;">$6 out of $12 -> $6/$12 = 0.5 = 50% 34 out of 100 -> 34/100 = 0.34 = 34% 0.55 = 55% 1.2 = 120%
 * //<span style="font-family: 'Verdana','sans-serif'; font-size: 10pt;">Examples //**

<span style="font-family: 'Verdana','sans-serif'; font-size: 10pt;">Find the value of n for each problem: <span style="font-family: 'Verdana','sans-serif'; font-size: 10pt;">n is 50% of 60 -> n = 0.5 x 60 = 30 n is 4% of 33 -> n = 0.04 x 33 = 1.32 n is 150% of 24 -> n = 1.5 x 24 = 36