NavGanitMateby NavGreen Compute, AustraliaBased on Victorian Curriculum Mathematics v2.0
← Back to practice

Percentage change and error

Wide tables scroll horizontally. For detailed working, you may prefer a larger screen.

Required skills (click to reveal)

A community garden in Adelaide plans to increase the area of its main vegetable plot by 78%. The original area of the plot is 89 square metres.

After the expansion, the gardeners measure the new area and record it as 158.22 square metres. Calculate the exact percentage error in the measured area compared to the actual calculated area.

Express your answer as an exact fraction in simplest form.

Concept illustrations

These are separate worked examples of related concepts, not a diagram of this question. Their values and dimensions do not describe your question.

Compare the increase with the original. A price grows from 80 to 100. The added 20 is one quarter of the original 80: a 25% increase. Bar lengths share the same scale.BeforeAfter80802020 ÷ 80 × 100% = 25%
A price grows from 80 to 100. The added 20 is one quarter of the original 80: a 25% increase. Bar lengths share the same scale.
A quarter is 25 percent. One of four equal parts is 25/100. For a whole of 80, each part is 20.1 of 4 equal parts
One of four equal parts is 25/100. For a whole of 80, each part is 20.

Press Start when ready. Time includes time spent in another tab. Submit your answer before opening a help panel for a timed rank.

00:00
0 wordsOnly your numerical final answer or selected MCQ option is checked. Scratch working is not graded.

Report a problem or suggest an improvement

My notes — optional, not graded 0 words

Notes and scratch working stay in this browser and are linked to this question version. They are not graded or included in feedback. On shared devices, other people using this browser may see them.

For this question only. Your full notebook is on the dashboard.

Notes save in this browser. Download a copy to keep them elsewhere.

Report a problem or suggest an improvement

Your observations help improve this question. You can report an issue or recommend a better explanation, visual or experience.

0 words

The report includes your message and question/version details. Saved profile details, answers, notes and attempt history are not automatically attached. Leave out names and contact details, and check screenshots for personal information and embedded metadata.

Attachments may contain personal information. Review them before sharing. Logs collect only event codes and timestamps after you enable them. Download the ZIP to keep a copy, then attach it to an email if you choose.

Formula and explanation (click to reveal)

Opening this before your first submission makes the attempt practice only.

Formula

Explanation

Worked solution and answer (click to reveal)

Opening this before your first submission makes the attempt practice only.

Worked solution

  1. The original area of the vegetable plot is 89 square metres. The garden plans a 78% increase, so the actual calculated area after expansion is 89 + (78% of 89).
  2. Convert 78% to a decimal by dividing by 100: 78 / 100 = 0.78.
  3. Calculate the increase: 0.78 × 89 = 69.42 square metres.
  4. Add the increase to the original area: 89 + 69.42 = 158.42 square metres. This is the actual calculated area.
  5. The measured area is 158.22 square metres. The actual calculated area is 158.42 square metres.
  6. Calculate the absolute error: |158.22 - 158.42| = 0.20 square metres.
  7. Percentage error is (absolute error / actual value) × 100. Use actual calculated area as the reference: (0.20 / 158.42) × 100.
  8. First compute 0.20 / 158.42 = 20 / 15842 (multiply numerator and denominator by 100 to eliminate decimal).
  9. Simplify 20 / 15842. Divide numerator and denominator by 2: 10 / 7921.
  10. Now compute (10 / 7921) × 100 = 1000 / 7921.
  11. The fraction 1000 / 7921 is already in simplest form because 1000 and 7921 share no common factors (7921 = 89², and 89 is prime, not dividing 1000).
  12. The exact percentage error is 1000 / 7921. This is the final answer as a simplified fraction.

Reference answer: 1000/7921

Alternative methods (click to reveal)

Shortcuts are shown only when applicable. Check the conditions before using one.

Earlier attempts for this question

#Date / timeYour answerResultSecondsHelp revealedRank
History stays in this browser when storage is available. Export it to your shared Drive folder and import it on another computer.
Worksheet details

Naming pattern: Topic_Grade_Complexity_YYYYMMDD_HH24MISS.html

Validation compares your answer with the generated reference. The model's reference can be wrong. Time ranks use an estimated student solving time, not a measured benchmark or a comparison with other students. An incorrect answer receives no speed rank.

NavGanitMate privacy & saved work

Saved in this browser. Your profile preferences, answers, practice history and notes are stored here when browser storage is available. They are not automatically uploaded to our servers. People sharing this browser may see saved work; changing the learner name does not create a separate private account. A nickname is enough.

Keep copies of important work. Clearing browser data, private browsing or changing browser or device can mean losing saved work. Download notes and export history separately. Downloads are copies of the selected content, not a complete account backup; not every format can be imported to restore your work. Keep these files somewhere private.

Visiting the website. Cloudflare helps deliver and protect this site and processes connection information such as IP addresses and requested pages. Server error logs may also contain request details. Security features may use cookies. This is separate from your browser-saved learning records. Cloudflare privacy information.

A parent-connection reminder uses a local list of up to five completed question IDs for this browser profile and a tab-session dismissal marker. Reminder activity is not uploaded and practice remains available.

Sharing feedback is your choice. A report includes your message and question/version details. Your saved profile, answers and notes are not automatically attached. Files you select can reveal personal details or contain embedded metadata: check and redact them before sharing. Diagnostic event codes and timestamps are included only after you enable logging. Sending email shares your message and attachments with the recipient and email providers. A download alone sends nothing to us. Website feedback delivery may be unavailable; only a confirmed receipt indicates it was received.