Final answer:
To estimate the decimal place in the quotient of 42.56 divided by 22, use simple close whole numbers like 40 divided by 20 which equals 2. The estimated answer is just above 2, placing the decimal to the right. Considering significant figures and rounding off is crucial for an accurate result.
Step-by-step explanation:
To estimate the placement of the decimal point in the quotient of 42.56 divided by 22, we look for whole numbers close to 42.56 and 22 that will simplify the arithmetic. A suitable estimation would be 40 divided by 20. Thus, 40 divided by 20 equals 2. We can now infer that the quotient of 42.56 divided by 22 will be slightly larger than 2, as 42.56 is a little more than 40 and 22 is a little more than 20. So, we estimate that the answer will be close to 2 but just above it. Therefore, we will place the decimal point to the right of the 2, making our estimated answer 2 point something.
Rounding off and significant figures are important concepts when computing with decimal numbers. When using a calculator to round to the appropriate number of significant figures, we must make sure not to report more decimal places than were present in the most precise measurement we began with. For instance, a calculator may provide several decimal places, but often we round off the result to only as many decimal places as the number in the problem with the least number of decimal places after the decimal point. Therefore, when dividing 42.56 by 22, we would not only place the decimal point accurately but also consider the number of significant figures in our final answer, rounding as necessary.