Question

. Find the percentage error when the number 4/3 is rounded-off to 1.33

Answer 1

Answer:

False

Step-by-step explanation:

$\frac{4}{3} \times 100$

$\frac{400}{3}$

$133.3$

Answer 2

Answer:

The percentage error when $\frac{4}{3}$ is rounded off to $1.33$ measured is $0.25\%$.

Step-by-step explanation:

Given,

The approximate/rounded-off value = $1.33$

The true value = $\frac{4}{3}$

The percentage error when $\frac{4}{3}$ is rounded off to $1.33$ =?

As we know,

• The relative error expressed in terms of percentage is known as the percentage error.
• Percentage error = Relative error × 100  

And,

• The relative error is the division of absolute error and true value.
• Relative error = $\frac{Absolute error}{True value}$

Also,

• The absolute error is the subtraction of the true value from the approximate value.
• Absolute error = | Approximate value - True value |

Hence,

1 ) Absolute error = | Approximate value - true value |

• Absolute error = | $1.33-\frac{4}{3}$ | = | $\frac{133}{100} - \frac{4}{3}$ | = | $\frac{399- 400}{300}$ | = $\frac{1}{300}$.

2 ) Relative error =  $\frac{Absolute error}{True value}$ =    $\frac{\frac{1}{300} }{\frac{4}{3} }$ = $\frac{1}{300}\times \frac{3}{4}$ = $0.0025$.

3 ) Percentage error = Relative error × 100

• Percentage error = $0.0025 \times 100$ = $0.25\%$.