Acc Pres Percent Error Half-Sheet | PDF - Free Printable

Let’s work through each part of the worksheet step by step.

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Part 1: Accuracy and Precision

We’re told the correct (true) value is 68.1 mL.

- Accurate means the measurements are close to the true value.
- Precise means the measurements are close to each other (even if not close to the true value).
- Both means they’re close to the true value AND close to each other.
- Neither means they’re far from the true value AND not close to each other.

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a) 78.1 mL, 43.9 mL, 2 mL

- Are they close to 68.1? → No. 78.1 is off by ~10, 43.9 is off by ~24, 2 is way off.
- Are they close to each other? → No. They range from 2 to 78.1 — very spread out.
→ So, neither

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b) 68.1 mL, 68.2 mL, 68.0 mL

- Close to 68.1? → Yes! All within 0.1 mL.
- Close to each other? → Yes! Only 0.2 mL apart max.
→ So, both

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c) 98.0 mL, 98.2 mL, 97.9 mL

- Close to 68.1? → No. All around 98 — that’s 30 mL off!
- Close to each other? → Yes! Within 0.3 mL of each other.
→ So, precise (but not accurate)

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d) 72.0 mL, 60.3 mL, 68.1 mL

- Close to 68.1? → One is exact (68.1), but others are off: 72.0 (+3.9), 60.3 (-7.8) — so mixed.
- Close to each other? → Range from 60.3 to 72.0 — that’s over 11 mL apart. Not precise.
→ Since only one is accurate and they’re not consistent, this is neither

*(Note: Some might argue “accurate” if you average them, but the question says “the set of measurements” — we look at individual values. None are consistently close, and they’re scattered. So “neither” is safest.)*

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Part 2: Percent Error Calculations

Formula for percent error:

> Percent Error = |Measured Value – True Value| / True Value × 100%

We always use absolute value (so no negative errors).

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1) Student measured string as 1.25 m. True length = 2.12 m

Error = |1.25 - 2.12| = 0.87
Percent Error = (0.87 / 2.12) × 100% ≈ ?

Calculate:
0.87 ÷ 2.12 = 0.41037...
× 100% = 41.0% → rounds to 41%

✔ Matches given answer.

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2) Teacher said volume = 500.0 mL. Student found 499.7 mL

Error = |499.7 - 500.0| = 0.3
Percent Error = (0.3 / 500.0) × 100% = ?

0.3 ÷ 500 = 0.0006
× 100% = 0.06%

✔ Matches given answer.

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3) Standard mass = 250.0 g. Balance read 243.9 g

Error = |243.9 - 250.0| = 6.1
Percent Error = (6.1 / 250.0) × 100% = ?

6.1 ÷ 250 = 0.0244
× 100% = 2.44% → rounds to 2.4%

✔ Matches given answer.

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4) Teacher calculated 54%. True value = 76%

Error = |54 - 76| = 22
Percent Error = (22 / 76) × 100% = ?

22 ÷ 76 ≈ 0.28947
× 100% ≈ 28.95% → rounds to 29%

✔ Matches given answer.

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5) Test had 34 questions. Best student got 22 correct.

Wait — what’s the “true value” here?

The question asks for percent error, which implies there’s a correct or expected score.

But it doesn’t say what the “correct” number of correct answers should be.

However, in testing contexts, sometimes “percent error” is misused — but let’s think logically.

If the student got 22 out of 34 correct, their score is (22/34) × 100% ≈ 64.7%.

But percent error requires a “true” or “accepted” value.

Looking at the provided answer: [35%]

How do we get 35%?

Maybe they mean: the student missed 12 questions (34 - 22 = 12).
Then, percent error = (number wrong / total questions) × 100%?

That would be: (12 / 34) × 100% ≈ 35.29% → 35%

Ah! So in this context, they’re treating “error” as the percentage of questions answered incorrectly.

Even though technically percent error usually compares measurement to true value, here since it’s a test, and no “true score” is given, they’re using:

> Percent Error = (Number Wrong / Total Questions) × 100%

Which is actually more like “percent incorrect,” but matches the expected answer.

So:

Wrong = 34 - 22 = 12
Percent Error = (12 / 34) × 100% ≈ 35.29% → 35%

✔ Matches given answer.

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Final Answers:

Part 1:
a) neither
b) both
c) precise
d) neither

Part 2:
1) 41%
2) 0.06%
3) 2.4%
4) 29%
5) 35%

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Final Answer:
a) neither
b) both
c) precise
d) neither
1) 41%
2) 0.06%
3) 2.4%
4) 29%
5) 35%