Question

While measuring a cl oth of length 2 meters, it was measured as 1.95 meters. Find the percentage error in measuring the cloth.

Answer 1

Answer:

Percentage error = 5%

Step-by-step explanation:

According to the information provided in the question it is given as

Cloth length = 2 meter

Measured  length = 1.95 meter

We need to find the % error

Difference of measurement = 2 - 1.95

                                              = 0.05

So the difference in length measurement  =0.05 meter

We used the formula of % for error

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. The formula used to calculate percentage is: (value/total value)×100%.

$\%=0.05\times 100\\=5\%$

So percentage error in measuring the cloth length is = 5%

Answer 2

Answer:

Percentage error = 2.5%

Step-by-step explanation:

In this problem we have given a 2 m long cloth, but it was measured as 1.95 m. Therefore, we have to find the percentage error while measuring the cloth.

Error = (approx value - exact value)/(exact value)

To find the error, first subtract the exact value of the cloth from the approx value then divide the resultant by exact value. Example: You thought there would be 9 sweets in a box, but there were actually 10. So, here the difference between approx value and exact value is -1. And absolute value of -1 is 1. Now, divide it by the exact value to find out the error. And if you looking for percentage value then multiply it by 100.

So,

Percentage error = (approx value - exact value)/(exact value) × 100

From above we can say that: exact value of the cloth is 2 m and approx value is 1.95 m. Simply, substitute the values.

Percentage error = (1.95 - 2)/2 × 100

= (-0.05)/2 × 100

Absolute value of -0.05 is 0.05 (|-0.05| = 0.05).

= 0.05/2 × 100

= 0.025 × 100

= 2.5%

Percentage error = 2.5%

[ Let's check if our percentage error is correct or not.

2.5% of 2 m length of cloth is 0.05 m.

= 2.5/100 × 2

= 2.5/50

= 0.05 m

Approx value of cloth was 1.95 m and from above 2.5% of 2 m length of cloth is 0.05 m. So, (0.05 + 1.95)m = 2 m. ]

Therefore, the percentage error is 2.5% while measuring a cloth.