Final answer:
In high school mathematics, to write a linear equation from data, coefficients are rounded to four decimal places. Numeric expressions such as 965 must be converted to scientific notation as 9.65 × 10². All answers must respect the correct number of significant figures and conversion of money must be rounded to the nearest penny.
Step-by-step explanation:
To determine the linear equation from a set of data, you need to first enter the data into a calculator or computer that has linear regression capabilities. Linear regression will help fit a line to your data, usually in the form of y = mx + b, where m is the slope and b is the y-intercept. Once you have the equation, you should round the coefficients to four decimal places as instructed.
For numeric transformations, such as changing 965 to a proper scientific notation, move the decimal point to the correct place to form a number between 1 and 10; for 965, this becomes 9.65. Then, count the number of places you moved the decimal to determine the exponent for the power of ten. In this case, 965 becomes 9.65 × 10².
When expressing answers, use the correct number of significant figures based on the precision of the measurements provided in the problem. For instance, if you're subtracting two measurements and the least precise has only two significant figures, your answer should be rounded to maintain that same level of precision.
For applications involving money, it's important to convert dollars and coins into dollars accurately. If working with dollar amounts and coins, sum up the values to express the total in dollars, making sure to round to the nearest cent (penny) when needed.