Question
Hal used the following procedure to find an estimate for √82.5.
Step 1: Since 9^2 = 81 and 10^2 = 100 and 81 < 82.5 < 100, then V82.5 is
between 9 and 10.
Step 2: Since 82.5 is closer to 81, square the tenths closer to 9
Step 2: Since 82.5 is closer to 81, square the tenths closer to 9
9.0^2 = 81.00
9.1^2 = 82.81
9.2^2 = 84.64
Step 3: Since 81.00 < 82.5 < 82.81, square the hundredths closer to 9.1
9.08^2 = 82.44
9.09^2 = 82.62
Step 4: Since 82.5 is closer to 82.62 than it is to 82.44, 9.09 is the best approximation for v82.5.
In which step did Hal make an error?
*
* Hal did not make an error.
* In step 4, he made an error in determining which value is closer to 82.5.
* In step 2, he made a calculation error when squaring.
O In step 1, V82.5 is between 8 and 10 because 82.5 ~ 80 and 8 × 10 = 80.
Step 1: Since 9^2 = 81 and 10^2 = 100 and 81 < 82.5 < 100, then V82.5 is
between 9 and 10.
Step 2: Since 82.5 is closer to 81, square the tenths closer to 9
Step 2: Since 82.5 is closer to 81, square the tenths closer to 9
9.0^2 = 81.00
9.1^2 = 82.81
9.2^2 = 84.64
Step 3: Since 81.00 < 82.5 < 82.81, square the hundredths closer to 9.1
9.08^2 = 82.44
9.09^2 = 82.62
Step 4: Since 82.5 is closer to 82.62 than it is to 82.44, 9.09 is the best approximation for v82.5.
In which step did Hal make an error?
*
* Hal did not make an error.
* In step 4, he made an error in determining which value is closer to 82.5.
* In step 2, he made a calculation error when squaring.
O In step 1, V82.5 is between 8 and 10 because 82.5 ~ 80 and 8 × 10 = 80.
Answers
Answered by
GPT-4o mini
Hal's procedure is mostly correct, but there is an error in Step 4.
In Step 4, he states that since 82.5 is closer to 82.62 than it is to 82.44, 9.09 is the best approximation for √82.5.
To clarify:
- 82.5 is exactly halfway between 82.44 and 82.62.
- The distance from 82.5 to 82.44 is 0.06, and the distance from 82.5 to 82.62 is also 0.12.
Since 0.06 is less than 0.12, the correct conclusion is that 9.08 (which gives 82.44) is a closer approximation to √82.5 than 9.09 (which gives 82.62).
Thus, the correct answer is: **In step 4, he made an error in determining which value is closer to 82.5.**
In Step 4, he states that since 82.5 is closer to 82.62 than it is to 82.44, 9.09 is the best approximation for √82.5.
To clarify:
- 82.5 is exactly halfway between 82.44 and 82.62.
- The distance from 82.5 to 82.44 is 0.06, and the distance from 82.5 to 82.62 is also 0.12.
Since 0.06 is less than 0.12, the correct conclusion is that 9.08 (which gives 82.44) is a closer approximation to √82.5 than 9.09 (which gives 82.62).
Thus, the correct answer is: **In step 4, he made an error in determining which value is closer to 82.5.**