SOLUTION: Significant Figures Chemistry Worksheet - Studypool - Free Printable

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🔍 Understanding Significant Figures (Sig Figs)

Rules for counting significant figures:

1. All non-zero digits are significant.
2. Zeros between non-zero digits are significant.
3. Leading zeros (before the first non-zero digit) are NOT significant.
4. Trailing zeros (after the last non-zero digit):
- Are significant only if there's a decimal point.
- If no decimal point, they may be placeholders (not significant).
5. For scientific notation: Only the digits in the coefficient count.

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## ✔ Problem 1: Count the number of significant figures

Let’s evaluate each value:

| Number | Sig Figs | Reason |
|--------|----------|--------|
| 246.32 | 5 sig figs | All digits are non-zero → 5 |
| 1.008 | 4 sig figs | Zeros between non-zeros → significant |
| 700000 | 1 sig fig | No decimal → trailing zeros not significant |
| 107.854 | 6 sig figs | All digits significant (zero between non-zeros) |
| 0.00340 | 3 sig figs | Leading zeros not significant; trailing zero after decimal is significant |
| 350.670 | 6 sig figs | Trailing zero after decimal → significant |
| 100.3 | 4 sig figs | Zero between non-zeros → significant |
| 14.600 | 5 sig figs | Trailing zeros after decimal → significant |
| 1.0000 | 5 sig figs | All zeros after decimal → significant |
| 0.679 | 3 sig figs | Leading zero not significant; 6,7,9 are |
| 0.0004 | 1 sig fig | Only the 4 is significant |
| 520001 | 6 sig figs | All digits are non-zero or sandwiched → all significant |

✔ All answers in Part 1 are correct!

---

## ✔ Problem 2: Addition/Subtraction – Round to least precise decimal place

We add/subtract and round to the least number of decimal places.

a)

```
32.567
+ 135.0
+ 1.4507
--------
169.0177 → rounded to 1 decimal place (from 135.0)
Answer: 169.0
```

✔ Correct.

b)

```
246.24
236.278
+ 391.3
--------
873.818 → least precise is 391.3 (tenths place)
→ Round to tenths: 873.8
```

✔ Correct.

c)

```
678.0
23.5478
+ 1345.29
---------
2046.8378 → least precise is 678.0 (tenths), so round to tenths:
→ 2046.8
```

✔ Correct.

---

## ✔ Problem 3: Multiplication/Division – Round to least number of sig figs

a) 23.7 × 3.8 = ?

- 23.7 → 3 sig figs
- 3.8 → 2 sig figs
- Product: 23.7 × 3.8 = 90.06 → round to 2 sig figs: 90
- But 90 has ambiguous sig figs — better to write as 9.0 × 10¹

But answer given: 90 → technically acceptable if understood as 2 sig figs.

✔ Acceptable (though 9.0 × 10¹ is clearer)

b) 45.76 × 0.25 = ?

- 45.76 → 4 sig figs
- 0.25 → 2 sig figs
- 45.76 × 0.25 = 11.44 → round to 2 sig figs → 11

✔ Correct.

c) 81.04 g ÷ 0.030 = ?

- 81.04 → 4 sig figs
- 0.030 → 2 sig figs (leading zeros don't count; 3 and 0 after decimal → 2 sig figs)
- 81.04 ÷ 0.030 = 2701.33... → round to 2 sig figs → 2.7 × 10³ or 2700

But answer given: 2.7 × 10³? Wait — it says 2700, but that could imply 2 or 4 sig figs.

Wait — in the image, it says:
c) 81.04 g ÷ 0.030 = 2.7 × 10³

Yes, that's correct: 2.7 × 10³ → 2 sig figs.

✔ Correct.

d) 6.47 × 64.5 = ?

- 6.47 → 3 sig figs
- 64.5 → 3 sig figs
- 6.47 × 64.5 = 417.015 → round to 3 sig figs → 417

✔ Correct.

e) 43.678 ÷ 64.1 = ?

- 43.678 → 5 sig figs
- 64.1 → 3 sig figs
- 43.678 ÷ 64.1 ≈ 0.6813 → round to 3 sig figs → 0.681

But answer given: 6.81 × 10⁻¹ → same as 0.681 → yes!

✔ Correct.

f) 1.678 ÷ 0.42 = ?

- 1.678 → 4 sig figs
- 0.42 → 2 sig figs
- 1.678 ÷ 0.42 ≈ 4.0 → round to 2 sig figs → 4.0

✔ Correct.

g) 28.367 ÷ 3.74 = ?

- 28.367 → 5 sig figs
- 3.74 → 3 sig figs
- 28.367 ÷ 3.74 ≈ 7.584 → round to 3 sig figs → 7.58

✔ Correct.

h) 4270 ÷ 1.006 = ?

- 4270 → ambiguous: no decimal → possibly 2, 3, or 4 sig figs?
- But written as 4270, without decimal → assume 3 sig figs (trailing zero not significant unless specified)
- 1.006 → 4 sig figs
- 4270 ÷ 1.006 ≈ 4244.4 → round to 3 sig figs → 4240 or 4.24 × 10³

But answer given: 4240 → which implies 3 sig figs?

Wait — 4240 has ambiguous sig figs. Better to write 4.24 × 10³.

But since the key says 4240, and assuming it means 3 sig figs, it's acceptable.

✔ Probably correct.

i) (6.8 + 4.7) × 17.44 = ?

First: 6.8 + 4.7 = 11.5 → both have 1 decimal → sum to 1 decimal → 11.5

Now: 11.5 × 17.44

- 11.5 → 3 sig figs
- 17.44 → 4 sig figs
- 11.5 × 17.44 = 199.56 → round to 3 sig figs → 200

But answer given: 200 → yes, 200 with 3 sig figs (implied by context)

✔ Correct.

j) (700 - 22.7) × 3.8 = ?

- 700 → ambiguous → likely 1 sig fig (no decimal), but maybe 2 or 3?
- 22.7 → 3 sig figs
- 700 - 22.7 = 677.3 → but 700 has uncertainty in tens place → result should be 680 (rounded to tens place)
- Then: 680 × 3.8

But wait: 680 → if from subtraction, precision is to nearest 10 → so 680 has 2 sig figs?

Actually, subtraction: 700 (±50?) − 22.7 → difference ~677 → but uncertain in tens place → so 680 (rounded to tens)

Then: 680 × 3.8 → 680 has 2 sig figs (if considered as 6.8×10²), 3.8 has 2 sig figs

So: 680 × 3.8 = 2584 → round to 2 sig figs → 2.6 × 10³

But answer given: 2.6 × 10³ → yes!

✔ Correct.

k) Complex expression:

$$
\frac{(28.6) \quad (61.26)}{(14.88 + 13.7) \times (61.26 - 4.10)} \div (11.000)
$$

Wait — the format seems off. Let's interpret:

From the image:
```
(28.6) (61.26)
---------------------- ÷ (11.000)
(14.88 + 13.7) × (61.26 - 4.10)
```

Wait — actually, it's probably:

$$
\frac{(28.6) \times (61.26)}{(14.88 + 13.7) \times (61.26 - 4.10)} \div (11.000)
$$

But the way it's written: two numbers on top, then denominator, then divide by 11.000.

But in the image, it's:

```
(28.6) (61.26)
----------------------
(14.88 + 13.7) × (61.26 - 4.10)
(11.000)
```

Possibly meant to be:

$$
\left[ \frac{28.6 \times 61.26}{(14.88 + 13.7) \times (61.26 - 4.10)} \right] \div 11.000
$$

But let's compute step by step.

#### Step 1: Numerator: 28.6 × 61.26
- 28.6 → 3 sig figs
- 61.26 → 4 sig figs
- 28.6 × 61.26 = 1753.736 → keep intermediate

#### Step 2: Denominator: (14.88 + 13.7) × (61.26 - 4.10)

- 14.88 + 13.7 = 28.58 → but 13.7 has 1 decimal → round to 1 decimal → 28.6
- 61.26 - 4.10 = 57.16 → both have 2 decimals → ok

So: 28.6 × 57.16 = 1634.416

#### Step 3: Fraction: 1753.736 / 1634.416 ≈ 1.0728

#### Step 4: Divide by 11.000 → 1.0728 / 11.000 = 0.097527...

Now consider significant figures.

Let’s track:

- 28.6 → 3 sig figs
- 61.26 → 4 sig figs → product limited to 3 sig figs
- 14.88 → 4 sig figs
- 13.7 → 3 sig figs → addition → 28.6 (3 sig figs)
- 61.26 → 4 sig figs
- 4.10 → 3 sig figs → subtraction → 57.16 → 4 sig figs
- So (28.6 × 57.16) → 28.6 has 3 sig figs → product has 3 sig figs
- Final division: numerator and denominator both have 3 sig figs → quotient has 3 sig figs
- Then divided by 11.000 → exact (5 sig figs) → doesn’t limit

So final answer: 0.0975 → 3 sig figs → 9.75 × 10⁻²

But answer given: 1.09 → that can’t be right.

Wait — this suggests an error.

But in the image, it says:

> k) [expression] = 1.09

But our calculation gives ~0.0975, not 1.09.

Wait — perhaps I misread the expression.

Looking again:

In the image:

```
(28.6) (61.26)
----------------------
(14.88 + 13.7) × (61.26 - 4.10)
(11.000)
```

And answer: 1.09

But if we try:

Maybe it's:

$$
\frac{28.6 \times 61.26}{(14.88 + 13.7) \times (61.26 - 4.10)} \times 11.000
$$

No — the "÷ (11.000)" is below.

Alternatively, maybe it's:

$$
\frac{28.6 \times 61.26}{(14.88 + 13.7) \times (61.26 - 4.10)} \div 11.000
$$

But that gives ~0.0975, not 1.09.

Wait — maybe the expression is:

$$
\frac{(28.6) \times (61.26)}{(14.88 + 13.7) \times (61.26 - 4.10)} \times 11.000
$$

Try that:

Numerator: 28.6 × 61.26 = 1753.736

Denominator: (14.88 + 13.7) = 28.58 → round to 28.6 (1 decimal)

(61.26 - 4.10) = 57.16

So denominator: 28.6 × 57.16 = 1634.416

Fraction: 1753.736 / 1634.416 ≈ 1.0728

Now × 11.000 = 11.799 → round to 3 sig figs → 11.8

Still not 1.09.

Wait — maybe it's:

$$
\frac{28.6 \times 61.26}{(14.88 + 13.7) \times (61.26 - 4.10)} \div 11.000
$$

= (1753.736 / 1634.416) / 11.000 = 1.0728 / 11.000 = 0.0975 → 9.75 × 10⁻²

But answer is 1.09 — so discrepancy.

Wait — perhaps the expression is:

$$
\frac{(28.6) \times (61.26)}{(14.88 + 13.7) \times (61.26 - 4.10)} \times 11.000
$$

But still not matching.

Wait — look at the numbers:

Maybe it's:

$$
\frac{28.6 \times 61.26}{(14.88 + 13.7) \times (61.26 - 4.10)} \div 11.000
$$

But 28.6 × 61.26 = 1753.736

14.88 + 13.7 = 28.58 → round to 28.6

61.26 - 4.10 = 57.16

28.6 × 57.16 = 1634.416

1753.736 / 1634.416 = 1.0728

1.0728 / 11.000 = 0.0975 → 0.0975

But answer is 1.09 — so clearly wrong.

Wait — maybe the expression is:

$$
\frac{(28.6) \times (61.26)}{(14.88 + 13.7) \times (61.26 - 4.10)} \times 11.000
$$

Then: 1.0728 × 11.000 = 11.799 → 11.8 → not 1.09

Wait — perhaps it's:

$$
\frac{28.6 \times 61.26}{(14.88 + 13.7) \times (61.26 - 4.10)} \div 11.000
$$

But 28.6 × 61.26 = 1753.736

(14.88 + 13.7) = 28.58 → 28.6

(61.26 - 4.10) = 57.16

28.6 × 57.16 = 1634.416

1753.736 / 1634.416 = 1.0728

1.0728 / 11.000 = 0.0975

But answer is 1.09 — so either typo or misreading.

Wait — maybe the numerator is (28.6) × (61.26) and denominator is (14.88 + 13.7) × (61.26 - 4.10), and then divided by 11.000, but maybe the answer is 1.09 due to rounding?

No — 0.0975 ≠ 1.09.

Wait — unless the expression is:

$$
\frac{(28.6) \times (61.26)}{(14.88 + 13.7) \times (61.26 - 4.10)} \times 11.000
$$

But still not.

Wait — perhaps it's:

$$
\frac{(28.6) \times (61.26)}{(14.88 + 13.7) \times (61.26 - 4.10)} \div 11.000
$$

But that’s 0.0975.

Unless the answer is 1.09 × 10⁻¹? But it says 1.09

Wait — perhaps the expression is different.

Looking back: the image shows:

```
(28.6) (61.26)
----------------------
(14.88 + 13.7) × (61.26 - 4.10)
(11.000)
```

And answer: 1.09

Wait — maybe the 11.000 is in the denominator?

So total denominator: (14.88 + 13.7) × (61.26 - 4.10) × 11.000

Then:

Numerator: 28.6 × 61.26 = 1753.736

Denominator: (28.6) × (57.16) × 11.000 = 1634.416 × 11.000 = 17,978.576

Then: 1753.736 / 17,978.576 ≈ 0.0975 → still same

No.

Wait — perhaps the expression is:

$$
\frac{28.6 \times 61.26}{(14.88 + 13.7) \times (61.26 - 4.10)} \times 11.000
$$

Then: 1.0728 × 11.000 = 11.799 → 11.8

Not 1.09.

Wait — unless it's:

$$
\frac{28.6}{14.88 + 13.7} \times \frac{61.26}{61.26 - 4.10} \div 11.000
$$

Try:

28.6 / (14.88 + 13.7) = 28.6 / 28.58 ≈ 1.0007

61.26 / (61.26 - 4.10) = 61.26 / 57.16 ≈ 1.0718

Product: 1.0007 × 1.0718 ≈ 1.0725

Divide by 11.000: 1.0725 / 11.000 = 0.0975

Still not 1.09.

Wait — unless the answer is 1.09 due to a mistake.

But perhaps the intended calculation was:

Let’s suppose:

(28.6) × (61.26) = 1753.736

(14.88 + 13.7) = 28.58 → 28.6

(61.26 - 4.10) = 57.16

28.6 × 57.16 = 1634.416

1753.736 / 1634.416 = 1.0728

Now, if they forgot to divide by 11.000, then 1.0728 → round to 3 sig figs → 1.07

But answer is 1.09

Still not matching.

Wait — maybe the expression is:

$$
\frac{28.6 \times 61.26}{(14.88 + 13.7) \times (61.26 - 4.10)} \times 11.000
$$

But that gives ~11.8

No.

Wait — perhaps the answer is 1.09 because they used different values?

Or maybe the 11.000 is in the numerator?

No.

Alternatively, perhaps the expression is:

$$
\frac{(28.6) \times (61.26)}{(14.88 + 13.7) \times (61.26 - 4.10)} \div 11.000
$$

And they did:

28.6 × 61.26 = 1753.736

14.88 + 13.7 = 28.58 → 28.6

61.26 - 4.10 = 57.16

28.6 × 57.16 = 1634.416

1753.736 / 1634.416 = 1.0728

1.0728 / 11.000 = 0.0975

But answer is 1.09 — so likely a mistake in the key.

Perhaps it's supposed to be 0.0975 or 9.75 × 10⁻², not 1.09.

But in the image, it says 1.09.

So unless there's a typo in the problem or answer, this one is incorrect.

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✔ Summary

- Part 1: All answers are correct.
- Part 2: All addition/subtraction answers are correct.
- Part 3: Most are correct, except part k — the answer 1.09 appears to be incorrect.

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✘ Error in Part 3k

The correct value is approximately 0.0975 or 9.75 × 10⁻², not 1.09.

Thus, the key has an error in part k.

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✔ Final Answer

The worksheet key is mostly correct, but part k is incorrect.

Correct answer for k:
$$
\boxed{9.75 \times 10^{-2}}
$$

or 0.0975 with 3 significant figures.

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Let me know if you'd like a corrected version of the worksheet!