Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Alex measures a line to be 7.72 in long. If the actual measurement is 8 in, find Alex's relative error to the nearest hundredth.
Answer:

Alex measures a line to be $7$ . $72$ in long. If the actual measurement is $8$ in, find Alex's relative error to the nearest hundredth. $\newline$ Answer:

View step-by-step help

View step-by-step help

Full solution

Q. Alex measures a line to be

7

.

72

in long. If the actual measurement is

8

in, find Alex's relative error to the nearest hundredth.

\newline

Answer:

Understand relative error: Understand the concept of relative error. Relative error is the absolute value of the difference between the measured value and the actual value, divided by the actual value. It is often expressed as a percentage.
Calculate absolute error: Calculate the absolute error, which is the difference between the actual measurement and Alex's measurement. $\newline$ Absolute error = $|\text{Actual measurement} - \text{Alex's measurement}|$ $\newline$ Absolute error = $|8 - 7.72|$ $\newline$ Absolute error = $|0.28|$ $\newline$ Absolute error = $0.28$
Calculate relative error: Calculate the relative error by dividing the absolute error by the actual measurement. $\newline$ Relative error = $\frac{\text{Absolute error}}{\text{Actual measurement}}$ $\newline$ Relative error = $\frac{0.28}{8}$ $\newline$ Relative error = $0.035$
Convert to percentage: Convert the relative error to a percentage and round to the nearest hundredth. $\newline$ Relative error (percentage) = Relative error $\times 100$ $\newline$ Relative error (percentage) = $0.035 \times 100$ $\newline$ Relative error (percentage) = $3.5\%$ $\newline$ Since we want the relative error to the nearest hundredth, we do not need to round further as it is already at the hundredth place.

More problems from Percent error

Question

An element with mass

230

grams decays by

27.7 \%

per minute. How much of the element is remaining after

8

minutes, to the nearest

1

\newline

Posted 2 months ago

Question

An element with mass

910

grams decays by

16.6 \%

per minute. How much of the element is remaining after

20

minutes, to the nearest

1

\newline

Posted 2 months ago

Question

An element with mass

990

grams decays by

18.8 \%

per minute. How much of the element is remaining after

13

minutes, to the nearest

1

\newline

Posted 2 months ago

Question

An element with mass

570

grams decays by

15.2 \%

per minute. How much of the element is remaining after

16

minutes, to the nearest

1

\newline

Posted 2 months ago

Question

An element with mass

490

grams decays by

18.8 \%

per minute. How much of the element is remaining after

8

minutes, to the nearest

1

\newline

Posted 2 months ago

Question

22

is increased to

39

. What is the percentage by which the number was increased, to the nearest tenth of a percent?

\newline

Posted 2 months ago

Question

35

is increased to

37

. What is the percentage by which the number was increased, to the nearest tenth of a percent?

\newline

Posted 2 months ago

Question

32

is increased to

35

. What is the percentage by which the number was increased, to the nearest tenth of a percent?

\newline

Posted 2 months ago

Question

33

is decreased to

32

. What is the percentage by which the number was decreased, to the nearest tenth of a percent?

\newline

Posted 2 months ago

Question

35

is decreased to

32

. What is the percentage by which the number was decreased, to the nearest tenth of a percent?

\newline

Posted 2 months ago