Significant Figures Practice Problems - Chemistry Steps - Free Printable

Let's solve each of these problems step by step, carefully applying the rules of arithmetic (addition, subtraction, multiplication, division) and paying attention to significant figures where appropriate.

---

a) 2.156 × 3.5

- Multiply:
$ 2.156 \times 3.5 = 7.546 $
- Significant figures:
- 2.156 has 4 sig figs
- 3.5 has 2 sig figs
→ Answer must have 2 significant figures
- Round 7.546 to 2 sig figs: 7.5

✔ Answer: 7.5

---

b) 7.05 × 5.9874

- Multiply:
$ 7.05 \times 5.9874 = 42.15627 $
- Significant figures:
- 7.05 → 3 sig figs
- 5.9874 → 5 sig figs
→ Limiting is 3 sig figs
- Round 42.15627 to 3 sig figs: 42.2

✔ Answer: 42.2

---

c) 12.5 ÷ 2.365

- Divide:
$ 12.5 \div 2.365 ≈ 5.285 $
- Significant figures:
- 12.5 → 3 sig figs
- 2.365 → 4 sig figs
→ Limiting is 3 sig figs
- Round 5.285 to 3 sig figs: 5.29

✔ Answer: 5.29

---

d) 24.2 + 17.56

- Add:
$ 24.2 + 17.56 = 41.76 $
- Decimal places:
- 24.2 → 1 decimal place
- 17.56 → 2 decimal places
→ Result should have 1 decimal place
- Round 41.76 to 1 decimal: 41.8

✔ Answer: 41.8

---

e) 124 + 11.78

- Add:
$ 124 + 11.78 = 135.78 $
- Decimal places:
- 124 → no decimal (or 0 decimal places)
- 11.78 → 2 decimals
→ Result must be rounded to no decimal places
- Round 135.78 → 136

✔ Answer: 136

---

f) 400 + 12.4

- Add:
$ 400 + 12.4 = 412.4 $
- Significant figures:
- 400 → ambiguous, but likely 1 sig fig if written as "400" (no decimal), or possibly 3? But in context, assume it's exact or has 1 sig fig unless specified.
- However, if we treat 400 as having no decimal, then precision is to units place
- 12.4 has 1 decimal place → so sum should be to nearest whole number
- So 412.4 → 412

But wait: 400 might be considered to have infinite precision (if it's a count), but here it’s likely exact or has uncertainty in units place.

Assuming 400 is precise to the tens place (i.e., ±10), then:
- 400 → uncertain in tens place
- 12.4 → certain to tenths
- Sum: 412.4 → but limited by 400’s precision

So final answer should be rounded to tens place:
→ 410

But if 400 is considered to have 3 sig figs (as in 400.), then it would be fine.

In most chemistry contexts, 400 without decimal implies 1 sig fig, but often treated as exact when used in addition.

Wait — for addition, we use decimal places, not sig figs.

- 400 → no decimal → precision to units place? But actually, 400 could mean 400±50 (if only 1 sig fig), or 400±1?

This is ambiguous.

But standard rule:
- If no decimal, trailing zeros are not significant
- So 400 has 1 sig fig, and its precision is to the hundreds place

Thus:
- 400 → uncertain in hundreds place → value is ~400±50
- 12.4 → known to tenths

So adding:
$ 400 + 12.4 = 412.4 $

But since 400 has uncertainty of ±50, the result should reflect that.

So the sum is 410 (rounded to nearest 10)

✔ Answer: 410

---

g) 13.4 + 0.79

- Add:
$ 13.4 + 0.79 = 14.19 $
- Decimal places:
- 13.4 → 1 decimal
- 0.79 → 2 decimals
→ Round to 1 decimal place
- 14.19 → 14.2

✔ Answer: 14.2

---

h) 65.418 – 34.25

- Subtract:
$ 65.418 - 34.25 = 31.168 $
- Decimal places:
- 65.418 → 3 decimals
- 34.25 → 2 decimals
→ Round to 2 decimal places
- 31.168 → 31.17

✔ Answer: 31.17

---

i) 52 + 23.54 + 0.0005

- Add:
$ 52 + 23.54 = 75.54 $
$ 75.54 + 0.0005 = 75.5405 $
- Now consider decimal places:
- 52 → no decimal → precision to units
- 23.54 → 2 decimals
- 0.0005 → 4 decimals
→ The least precise is 52 → units place
- So round 75.5405 to nearest unit:
→ 76

✔ Answer: 76

---

j) 251 – 0.359

- Subtract:
$ 251 - 0.359 = 250.641 $
- 251 → no decimal → precision to units
- 0.359 → 3 decimals
- So result must be to units place
- Round 250.641 → 251

✔ Answer: 251

---

k) 250 + 1,700 + 465.1

- Add:
$ 250 + 1700 = 1950 $
$ 1950 + 465.1 = 2415.1 $
- Now check precision:
- 250 → no decimal → units place
- 1700 → no decimal → tens place?
- 1700 → could be ±50 or ±10? Ambiguous
- 465.1 → 1 decimal → precise to tenths

But for addition, we go by least precise decimal place

- 250 → precision to units
- 1700 → precision to tens (since no decimal)
- 465.1 → precision to tenths

So least precise is tens place (from 1700)

Therefore, round total to tens place:

- 2415.1 → 2420 (rounded to nearest 10)

✔ Answer: 2420

---

l) 3,400.00 × 0.624 + 230

We need to follow order of operations (PEMDAS): multiply first, then add.

#### Step 1: $ 3,400.00 \times 0.624 $

- $ 3,400.00 \times 0.624 = 2,121.6 $
- Sig figs:
- 3,400.00 → 6 sig figs
- 0.624 → 3 sig figs
→ Product has 3 sig figs
- Round 2,121.6 → 2,120 (3 sig figs)

Now add 230:

- $ 2,120 + 230 = 2,350 $
- Now check decimal places:
- 2,120 → no decimal → precision to tens
- 230 → no decimal → also tens
→ So sum to tens place
- 2,350 → already at tens place

✔ Answer: 2,350

---

m) $ \frac{4.2 + 3.987 + 0.645}{2.64} $

#### Numerator:
$ 4.2 + 3.987 + 0.645 = 8.832 $

- Decimal places:
- 4.2 → 1 decimal
- 3.987 → 3 decimals
- 0.645 → 3 decimals
→ Limited by 4.2 → 1 decimal
- So numerator → 8.8

Now divide:
$ 8.8 \div 2.64 ≈ 3.333... $

- Now sig figs:
- 8.8 → 2 sig figs
- 2.64 → 3 sig figs
→ Result should have 2 sig figs
- 3.333 → 3.3

✔ Answer: 3.3

---

n) $ \frac{5.874 \times 3.28}{19.4 - 16.70} $

#### Step 1: Numerator: $ 5.874 \times 3.28 $

- $ 5.874 \times 3.28 = 19.23472 $
- Sig figs:
- 5.874 → 4 sig figs
- 3.28 → 3 sig figs
→ Product has 3 sig figs
- Round: 19.23472 → 19.2

#### Step 2: Denominator: $ 19.4 - 16.70 $

- $ 19.4 - 16.70 = 2.7 $
- Decimal places:
- 19.4 → 1 decimal
- 16.70 → 2 decimals
→ Result to 1 decimal
- 2.7 → correct

Now divide:
$ 19.2 \div 2.7 ≈ 7.111... $

- Sig figs:
- 19.2 → 3 sig figs
- 2.7 → 2 sig figs
→ Result has 2 sig figs
- Round 7.111 → 7.1

✔ Answer: 7.1

---

o) $ \frac{8.3 - 2.354 + 0.57}{2} $

#### Numerator: $ 8.3 - 2.354 + 0.57 $

Step-by-step:

- $ 8.3 - 2.354 = 5.946 $
- $ 5.946 + 0.57 = 6.516 $

Now decimal places:
- 8.3 → 1 decimal
- 2.354 → 3 decimals
- 0.57 → 2 decimals
→ Least precise is 1 decimal (8.3)

So numerator → 6.5

Now divide by 2:

- $ 6.5 \div 2 = 3.25 $
- But 2 is exact (count), so we keep sig figs from 6.5 → 2 sig figs
- 3.25 → round to 3.3 (2 sig figs)

✔ Answer: 3.3

---

p) $ \frac{85.3 - 21.489}{0.0059} $

#### Numerator: $ 85.3 - 21.489 = 63.811 $

- Decimal places:
- 85.3 → 1 decimal
- 21.489 → 3 decimals
→ Result to 1 decimal: 63.8

Denominator: 0.0059 → 2 sig figs

Now divide:
$ 63.8 \div 0.0059 ≈ 10,813.56 $

- Sig figs:
- 63.8 → 3 sig figs
- 0.0059 → 2 sig figs
→ Result has 2 sig figs
- Round 10,813.56 → 1.1 × 10⁴

✔ Answer: 1.1 × 10⁴

---

q) $ \frac{3.654}{2.2} + \frac{0.438}{0.670} + \frac{60.948}{0.3716} $

Solve each fraction:

#### 1. $ \frac{3.654}{2.2} = 1.65909... $
- Sig figs: 3.654 → 4, 2.2 → 2 → 2 sig figs
- → 1.7

#### 2. $ \frac{0.438}{0.670} = 0.6537... $
- Sig figs: both have 3 → 3 sig figs
- → 0.654

#### 3. $ \frac{60.948}{0.3716} = 164.02... $
- 60.948 → 5 sig figs
- 0.3716 → 4 sig figs
- → 4 sig figs → 164.0

Now add:
$ 1.7 + 0.654 + 164.0 = 166.354 $

Now consider decimal places:
- 1.7 → 1 decimal
- 0.654 → 3 decimals
- 164.0 → 1 decimal
→ Least precise is 1 decimal

So round to 1 decimal: 166.4

✔ Answer: 166.4

---

r) $ \frac{7.456 \times (4.12 + 3.59874)}{5.874} $

#### Step 1: Inside parentheses: $ 4.12 + 3.59874 = 7.71874 $

- Decimal places:
- 4.12 → 2 decimals
- 3.59874 → 5 decimals
→ Result to 2 decimals: 7.72

#### Step 2: Multiply: $ 7.456 \times 7.72 $

- $ 7.456 \times 7.72 = 57.54592 $
- Sig figs:
- 7.456 → 4 sig figs
- 7.72 → 3 sig figs
→ Result → 3 sig figs
- → 57.5

#### Step 3: Divide by 5.874

- $ 57.5 \div 5.874 ≈ 9.789 $
- Sig figs:
- 57.5 → 3 sig figs
- 5.874 → 4 sig figs
→ Result → 3 sig figs
- → 9.79

✔ Answer: 9.79

---

## ✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| a) | 7.5 |
| b) | 42.2 |
| c) | 5.29 |
| d) | 41.8 |
| e) | 136 |
| f) | 410 |
| g) | 14.2 |
| h) | 31.17 |
| i) | 76 |
| j) | 251 |
| k) | 2420 |
| l) | 2,350 |
| m) | 3.3 |
| n) | 7.1 |
| o) | 3.3 |
| p) | 1.1 × 10⁴ |
| q) | 166.4 |
| r) | 9.79 |

Let me know if you'd like this in a table format or with more explanation on any step!