Question 1-Battery%0D%0AAlmost everyone these days has a portable technological device, like a cell phone, %0D%0Alaptop, video game console, or music player. We charge these devices so that we can %0D%0Ause them on the go. The amount of remaining battery is usually represented as a %0D%0Apercentage. %0D%0Aa. Choose one or more of these devices that you (or a friend or family member) %0D%0Aown, and look at the current battery level. Convert this percentage into a %0D%0Adecimal and a simplified fraction.%0D%0Ab. After about 1,000 charging cycles, smartphone batteries lose about one fifth of %0D%0Atheir charging capacity. A brand new phone is currently at 78%. What would %0D%0Athis phone’s battery percentage show after 1,000 charging cycles? After 500?%0AQuestion 2-Gas Prices%0D%0AIn the U.S. currency system, we represent monetary values with dollars and cents. %0D%0ABecause there are 100 cents in a dollar, monetary amounts are represented with at %0D%0Amost two decimal places. Gas prices are often shown to have more than two decimal %0D%0Aplaces. Find the local price of gas, and use that information to answer the following %0D%0Aquestions. Show all work.%0D%0Aa. Express the determined gas price as a dollar amount rounded to the nearest %0D%0Acent. Why do you think gas companies choose to show these prices into the %0D%0Athousandth and ten-thousandth place when we do not have currency to pay %0D%0Athese exact amounts?%0D%0Ab. The price displayed at a gas station is the price per gallon. What is the smallest %0D%0Anumber of gallons of gas you would have to buy for the price of the gas to %0D%0Ahave a whole number of cents? A whole number of dollars?%0D%0Ac. Express the price per gallon of gas as a mixed number.%0AQuestion 3-Interest Rates%0D%0AMoney that is kept in the bank earns interest. Interest is money paid to bank account %0D%0Aholders in repayment for allowing the bank to loan out their money. Interest rates are %0D%0Arepresented as a percentage of the amount of money in the bank account. Use this %0D%0Ainformation to answer the following questions.%0D%0Aa. Research a local bank, and determine their interest rate. Imagine you have a %0D%0Abank account with $10,000 in it. How much interest would you earn after the %0D%0Afirst year? How did you arrive at this number? Did you leave the interest rate %0D%0Aas a percentage, or did you convert it into a fraction or decimal? Explain
a. To convert the current battery percentage into a decimal, divide the percentage by 100. For example, if the battery level is 50%, the decimal would be 0.50. To convert it into a simplified fraction, divide the percentage by 100 and simplify if possible. For example, if the battery level is 75%, the simplified fraction would be 3/4.
b. After 1,000 charging cycles, a smartphone battery loses one fifth of its charging capacity. To calculate the battery percentage after 1,000 cycles, multiply the current percentage (78%) by four fifths (4/5). After 500 charging cycles, multiply the current percentage by two fifths (2/5).
c. Gas prices are often shown with more decimal places for precision and to reflect the large volume of transactions in the gas industry. While we do not have currency denominations for these exact amounts, showing them allows for more accurate calculations and comparisons.
d. To determine the smallest number of gallons of gas to get a whole number of cents, divide 1 by the gas price in dollars (rounded to the nearest cent). To get a whole number of dollars, divide 100 by the gas price in cents.
e. To express the price per gallon of gas as a mixed number, divide the gas price in dollars by the gas price in cents. The whole number part represents the dollar amount, and the fractional part represents the remaining cents.
In order to answer these questions, you will need to conduct some research and gather specific information. Here are some examples to help guide you in answering each question:
Question 1:
a. Choose a device: Let's say you choose a cell phone and the current battery level is 60%. To convert this percentage into a decimal, you divide it by 100: 60 / 100 = 0.6. To convert it into a simplified fraction, you can express it as 3/5.
b. After 1,000 charging cycles, the phone's battery would lose one-fifth of its charging capacity. To calculate this, you multiply the initial battery level (78%) by 4/5: 78 * 4/5 = 62.4%. After 1,000 charging cycles, the phone's battery percentage would show 62.4%. To calculate the battery level after 500 charging cycles, you multiply the initial battery level (78%) by 2/5: 78 * 2/5 = 31.2%. After 500 charging cycles, the phone's battery percentage would show 31.2%.
Question 2:
a. Find the local gas price and express it as a dollar amount rounded to the nearest cent. For example, if the gas price is $2.579 per gallon, you would round it to $2.58.
b. In order for the price of gas to have a whole number of cents, you would need to buy a whole number of gallons. For example, if the gas price is $2.58 per gallon, you would need to buy at least 100 gallons to have a whole number of cents (100 * $2.58 = $258). To have a whole number of dollars, you would need to buy at least 1 gallon.
c. To express the price per gallon as a mixed number, divide the gas price by 1 dollar. For example, if the gas price is $2.58 per gallon, you would have 2 and 58/100 dollars per gallon.
Question 3:
a. Research a local bank and determine their interest rate. Let's say the interest rate is 2.5%. To calculate the amount of interest you would earn after the first year on $10,000, you can multiply the initial amount by the interest rate (as a decimal): $10,000 * 0.025 = $250. You can leave the interest rate as a percentage for this calculation.
Remember to consult reliable sources and adjust the calculations according to the specific information you gather.
Question 1:
a) To convert the battery percentage into a decimal, divide the percentage value by 100. For example, if the battery percentage is 70%, the decimal value would be 0.70.
To convert the decimal into a simplified fraction, write it as a fraction with the decimal value as the numerator and 1 as the denominator. Then simplify the fraction if possible. For example, using the decimal value 0.70, the fraction would be 70/100, which simplifies to 7/10.
b) After 1,000 charging cycles, a smartphone battery loses one fifth (1/5) of its charging capacity. To find the battery percentage after 1,000 cycles, subtract one fifth (1/5) of the current battery percentage.
Assuming the current battery percentage is 78%, subtracting 1/5 of 78%:
78% - (1/5) * 78% = 78% - 0.2 * 78% = 78% - 0.156 = 77.844%
After 1,000 charging cycles, the phone's battery percentage would show approximately 77.844%.
After 500 charging cycles, use the same formula:
78% - (1/5) * (1/2) * 78% = 78% - 0.1 * 78% = 78% - 0.078 = 77.922%
After 500 charging cycles, the phone's battery percentage would show approximately 77.922%.
Question 2:
a) To express the gas price as a dollar amount rounded to the nearest cent, look at the price per gallon and round it to the nearest cent. For example, if the price per gallon is $2.456, rounded to the nearest cent it becomes $2.46.
Gas companies choose to show prices to the thousandth and ten-thousandth place for several reasons. Firstly, it allows for more precise pricing comparisons between gas stations. Additionally, some fuel retailers use advanced fuel dispensers that can measure fuel quantities to the thousandth or ten-thousandth of a gallon. Showing more decimal places also gives the impression of accuracy and attention to detail.
b) To determine the smallest number of gallons of gas that would have a whole number of cents, divide 100 by the price per gallon and take the ceiling of the result. For example, if the gas price is $2.46 per gallon:
100 / 2.46 = 40.65 (rounded to two decimal places)
The ceiling of 40.65 is 41. Therefore, the smallest number of gallons of gas you would have to buy for the price to have a whole number of cents is 41 gallons.
To determine the smallest number of gallons of gas that would have a whole number of dollars, divide 100 by the price per gallon and take the floor of the result. Using the same example:
100 / 2.46 = 40.65 (rounded to two decimal places)
The floor of 40.65 is 40. Therefore, the smallest number of gallons of gas you would have to buy for the price to have a whole number of dollars is 40 gallons.
c) To express the price per gallon of gas as a mixed number, divide the price per gallon by 1 and express the result as a mixed number. For example, if the price per gallon is $2.46:
2.46 / 1 = 2 remainder 0.46
The mixed number representation would be 2 and 46/100.
Question 3:
a) Research a local bank and determine their interest rate. Let's assume the bank's interest rate is 2.5% per annum. To calculate the interest earned after the first year on a $10,000 bank account, multiply the interest rate by the principal amount:
$10,000 * 2.5% = $250
We arrived at this number by converting the interest rate into a decimal (2.5% = 0.025) and then multiplying it by the principal amount. The interest rate was converted into a decimal by dividing it by 100 (2.5% / 100 = 0.025).
b) I apologize, but it seems there is no continuation to the question in regards to this matter. If you have any other questions, feel free to ask!