Given that a= 6.3, b=14.2, and d=0.0173. Find the percentage error in ab÷cd
To find the percentage error in the expression ab ÷ cd, we will first calculate the actual value of ab ÷ cd and the approximate value by considering the given values with their percentage errors. Then we can compare the two values to find the percentage error.
Given values:
a = 6.3 (with no percentage error)
b = 14.2 (with no percentage error)
d = 0.0173 (with no percentage error)
First, we can calculate the actual value of ab ÷ cd:
ab ÷ cd = (6.3 * 14.2) ÷ (0.0173)
Actual value = 6.3 * 14.2 ÷ 0.0173
Now, we need to calculate the approximate value by considering the percentage errors:
Suppose a has a percentage error of 1%, b has a percentage error of 2%, and d has a percentage error of 3%.
a_with_error = a * (1 + 1/100) = 6.3 * (1 + 1/100)
b_with_error = b * (1 + 2/100) = 14.2 * (1 + 2/100)
d_with_error = d * (1 + 3/100) = 0.0173 * (1 + 3/100)
Then, we can calculate the approximate value of ab ÷ cd with the given percentage errors:
ab ÷ cd (approximate) = (a_with_error * b_with_error) ÷ d_with_error
Approximate value = (6.3 * (1 + 1/100) * 14.2 * (1 + 2/100)) ÷ (0.0173 * (1 + 3/100))
Now, we can calculate the percentage error:
Percentage error = ((Actual value - Approximate value) / Actual value) * 100
Substitute the actual and approximate values to find the percentage error.