Consider the following method of estimating
Fahrenheit temperatures given Celsius temperatures
(which was stated earlier in this section):
To estimate the Fahrenheit temperature for a given Celsius
temperature, double the Celsius temperature and add 30.
Create a spreadsheet comparing the estimates with the
actual Fahrenheit temperatures for Celsius temperatures
from 0 to 40°. (The estimate can be expressed as follows:F = 2C + 30
.) For what temperatures is the estimate
most accurate? least accurate? Are there any Celsius temperatures
for which the estimate is exactly correct?
In Excel, I would create 3 columns
Put 0 into A1
in B1 type: A1*2 + 30
in C1 type : A1*(9/5) + 32
in A2 type : =A1 + 1
select A2 to A101, "fill down"
"fill down" the values for columns B and C from 1 to 101
as a check: my values for 20 are 70 and 68
and at 10º F I get 50 in both columns
To create a spreadsheet comparing the estimates with the actual Fahrenheit temperatures, you can follow these steps:
1. Open a spreadsheet software like Microsoft Excel or Google Sheets.
2. Create two columns: one for the Celsius temperatures and one for the estimated Fahrenheit temperatures.
3. In the first row of the Celsius column, start with the value 0 (representing 0°C).
4. In the corresponding cell of the estimated Fahrenheit column (e.g., B1), enter the formula "=2*A1+30" to calculate the estimated Fahrenheit temperature for the given Celsius temperature, assuming the Celsius temperature is in cell A1.
5. Drag the formula down to fill the remaining cells in the estimated Fahrenheit column.
6. Repeat steps 3-5 for Celsius temperatures from 1 to 40.
Once you have filled in the spreadsheet with the estimated Fahrenheit temperatures, you can compare them with the actual Fahrenheit temperatures to identify the most accurate and least accurate temperatures.
To determine the temperatures where the estimate is most accurate, you can calculate the difference between the estimate and the actual Fahrenheit temperature for each Celsius temperature and find the smallest differences.
To determine the least accurate temperatures, you can calculate the difference between the estimate and the actual Fahrenheit temperature for each Celsius temperature and find the largest differences.
The estimate will be exactly correct for certain Celsius temperatures if the estimated Fahrenheit temperature matches the actual Fahrenheit temperature. Check if any Celsius temperature in your spreadsheet has an exact match between the estimated and actual Fahrenheit temperatures.
By analyzing the spreadsheet, you can answer the specific questions about the most accurate, least accurate, and exact matches based on the values calculated for the Celsius and estimated Fahrenheit columns.