A student multiplied a number by
7
4
instead of
4
7
. What is the percentage error in the calculation?
- A206.25 percent
- B67.35 percent
- C33.67 percent
- D103.13 percent
Solution & Step-by-step Explanation
Let the number be x. For simplicity, let's assume the number is the LCM of the denominators 4 and 7, which is 28.
Correct calculation: 28×
4
7
=49
Incorrect calculation: 28×
7
4
=16
The error in calculation is:
Error=Correct Value−Incorrect Value=49−16=33
The percentage error is calculated relative to the correct value:
Percentage Error=(
Correct Value
Error
)×100
Percentage Error=(
49
33
)×100=
49
3300
≈67.346%≈67.35%
Correct calculation: 28×
4
7
=49
Incorrect calculation: 28×
7
4
=16
The error in calculation is:
Error=Correct Value−Incorrect Value=49−16=33
The percentage error is calculated relative to the correct value:
Percentage Error=(
Correct Value
Error
)×100
Percentage Error=(
49
33
)×100=
49
3300
≈67.346%≈67.35%