chemistry
worksheet - scientific notation, significant figures, units & conversions
1. write each of the following numbers in proper scientific notation.
a) 450,000
b) 0.00000982
c) 6.906
2. determine how many significant figures are in each of the following measurements.
a) 17.30 ml
b) 0.0037 mm
c) 3.05 × 10³ kg
3. round each of the following measurements to three significant figures.
a) 18.75 °c
b) 4.8015 g/ml
c) 0.002955 km
4. perform each of the following calculations. write the answer given by your calculator on the first blank and then round to the appropriate number of significant figures on the second blank.
a) 0.57 cm × 0.86 cm × 17.1 cm =
b) 4.153 cm ÷ 1.81 cm =
c) 0.64 m × 14.8 m × 50.0 m =
5. convert each of the following measurements.
a) convert 0.410 m to cm
b) convert 32.8 ml to l
c) convert 2.51 km to mm
name __________
period __ date ______

Question

chemistry
worksheet - scientific notation, significant figures, units & conversions
1. write each of the following numbers in proper scientific notation.
   a) 450,000
   b) 0.00000982
   c) 6.906
2. determine how many significant figures are in each of the following measurements.
   a) 17.30 ml
   b) 0.0037 mm
   c) 3.05 × 10³ kg
3. round each of the following measurements to three significant figures.
   a) 18.75 °c
   b) 4.8015 g/ml
   c) 0.002955 km
4. perform each of the following calculations. write the answer given by your calculator on the first blank and then round to the appropriate number of significant figures on the second blank.
   a) 0.57 cm × 0.86 cm × 17.1 cm =
   b) 4.153 cm ÷ 1.81 cm =
   c) 0.64 m × 14.8 m × 50.0 m =
5. convert each of the following measurements.
   a) convert 0.410 m to cm
   b) convert 32.8 ml to l
   c) convert 2.51 km to mm
name __________
period __ date ______

Accepted Answer

### Question 1: Write each number in proper scientific notation
#### Part A: 450,000
# Explanation:
## Step 1: Move decimal to get $ 1 \leq a < 10 $
Move decimal 5 places left: $ 450000 = 4.5 \times 10^5 $

#### Part B: 0.00000982
# Explanation:
## Step 1: Move decimal to get $ 1 \leq a < 10 $
Move decimal 6 places right: $ 0.00000982 = 9.82 \times 10^{-6} $

#### Part C: 6.906
# Explanation:
## Step 1: Check if $ 1 \leq a < 10 $
$ 6.906 $ is already in range, so $ 6.906 = 6.906 \times 10^0 $

### Question 2: Determine significant figures
#### Part A: 17.30 mL
# Explanation:
- Non - zeros (1,7,3) are significant.
- Trailing zero after decimal is significant.
Total: 4 sig. figs.

#### Part B: 0.0037 mm
# Explanation:
- Leading zeros are not significant.
- 3 and 7 are significant.
Total: 2 sig. figs.

#### Part C: $ 3.05 \times 10^3 $ kg
# Explanation:
- In scientific notation, digits in $ a $ (3,0,5) are significant.
Total: 3 sig. figs.

### Question 3: Round to three significant figures
#### Part A: $ 18.75^\circ \text{C} $
# Explanation:
## Step 1: Identify third sig. fig (7) and next digit (5)
## Step 2: Round up (5 ≥ 5)
$ 18.75
ightarrow 18.8 $ (three sig. figs)

#### Part B: 4.8015 g/mL
# Explanation:
## Step 1: Identify third sig. fig (0) and next digit (1)
## Step 2: Round down (1 < 5)
$ 4.8015
ightarrow 4.80 $ (three sig. figs)

#### Part C: 0.002955 km
# Explanation:
## Step 1: Identify third sig. fig (5) and next digit (5)
## Step 2: Round up
$ 0.002955
ightarrow 0.00296 $ (three sig. figs)

### Question 4: Perform calculations (calculator value → rounded)
#### Part A: $ 0.57 \, \text{cm} \times 0.86 \, \text{cm} \times 17.1 \, \text{cm} $
# Explanation:
## Step 1: Calculator value
$ 0.57 \times 0.86 = 0.4902 $; $ 0.4902 \times 17.1 = 8.38242 $
## Step 2: Round (least sig. figs: 2 (0.57, 0.86) → 2 sig. figs? Wait, 0.57 (2), 0.86 (2), 17.1 (3) → least is 2? No, multiplication/division: round to least sig. figs. Wait, 0.57 (2), 0.86 (2), 17.1 (3) → 2 sig. figs? Wait, no: 0.57 (2), 0.86 (2), 17.1 (3) → the result should have 2 sig. figs? Wait, no, 0.57 and 0.86 have 2, 17.1 has 3. So the least is 2? Wait, no, 0.57 (2), 0.86 (2), 17.1 (3). So when multiplying, the number of sig. figs is determined by the least, which is 2? Wait, no, 0.57 is two, 0.86 is two, 17.1 is three. So the product should have two sig. figs? Wait, no, 0.57 × 0.86 = 0.4902 (two sig. figs? No, 0.57 and 0.86 have two, so their product has two: 0.49 (but 0.4902 rounded to two sig. figs is 0.49? No, 0.4902 → 0.49 (two sig. figs) or 0.490 (three)? Wait, no, 0.57 (two sig. figs: 5 and 7), 0.86 (two: 8 and 6). So 0.57 × 0.86 = 0.4902, which should be rounded to two sig. figs: 0.49? No, 0.4902 → 0.49 (two sig. figs) is 0.49, but then ×17.1 (three sig. figs). Wait, maybe I made a mistake. Let's recalculate: 0.57 × 0.86 = 0.4902; 0.4902 × 17.1 = 8.38242. Now, the least number of sig. figs in the factors is 2 (from 0.57 and 0.86). So we round 8.38242 to two sig. figs: 8.4? Wait, 8.38242 → 8.4 (two sig. figs? No, 8.4 has two? Wait, 8 is first sig. fig, 4 is second. So 8.4 (two sig. figs). Wait, but 0.57 is two, 0.86 is two, 17.1 is three. So the rule is: for multiplication/division, the result has the same number of sig. figs as the least precise measurement. So 2 sig. figs. So 8.38242 → 8.4 (two sig. figs? Wait, 8.38242 rounded to two sig. figs: look at the third digit, 8 ≥ 5, so round up the second digit: 8.4 (since 8.38242 → 8.4 when rounded to two sig. figs? Wait, 8.38242: first sig. fig 8, second 3, third 8. So to two sig. figs: 8.4 (because 3 + 1 = 4 when we round up the third digit 8). Yes. So calculator value: 8.38242; rounded: 8.4 (or maybe 8.4 with two sig. figs? Wait, no, 8.4 has two sig. figs? Wait, 8 is one, 4 is two. Yes.

#### Part B: $ 4.153 \, \text{cm} \div 1.81 \, \text{cm} $
# Explanation:
## Step 1: Calculator value
$ 4.153 \div 1.81 \approx 2.294475 $
## Step 2: Round (least sig. figs: 3 (4.153) and 3 (1.81) → 3 sig. figs)
$ 2.294475
ightarrow 2.29 $ (three sig. figs)

#### Part C: $ 0.64 \, \text{m} \times 14.8 \, \text{m} \times 50.0 \, \text{m} $
# Explanation:
## Step 1: Calculator value
$ 0.64 \times 14.8 = 9.472 $; $ 9.472 \times 50.0 = 473.6 $
## Step 2: Round (least sig. figs: 2 (0.64), 3 (14.8), 3 (50.0) → 2 sig. figs)
$ 473.6
ightarrow 470 $ (or $ 4.7 \times 10^2 $)? Wait, 0.64 has two sig. figs, so the result should have two. 473.6 → 470 (two sig. figs: 4 and 7, the trailing zero is not significant here? Wait, no, 470 with two sig. figs is $ 4.7 \times 10^2 $. But maybe the problem expects 470 (if we consider 473.6 rounded to two sig. figs: 470 (since the third digit is 3 < 5, so we keep the second digit 7 and replace the rest with zeros, but in scientific notation, it's $ 4.7 \times 10^2 $).

### Question 5: Unit conversions
#### Part A: Convert 0.410 m to cm
# Explanation:
## Step 1: Conversion factor ($ 1 \, \text{m} = 100 \, \text{cm} $)
$ 0.410 \, \text{m} \times \frac{100 \, \text{cm}}{1 \, \text{m}} = 41.0 \, \text{cm} $

#### Part B: Convert 32.8 mL to L
# Explanation:
## Step 1: Conversion factor ($ 1 \, \text{L} = 1000 \, \text{mL} $)
$ 32.8 \, \text{mL} \times \frac{1 \, \text{L}}{1000 \, \text{mL}} = 0.0328 \, \text{L} $ (or $ 3.28 \times 10^{-2} \, \text{L} $)

#### Part C: Convert 2.51 km to mm
# Explanation:
## Step 1: Conversion factors ($ 1 \, \text{km} = 1000 \, \text{m} $, $ 1 \, \text{m} = 1000 \, \text{mm} $)
$ 2.51 \, \text{km} \times \frac{1000 \, \text{m}}{1 \, \text{km}} \times \frac{1000 \, \text{mm}}{1 \, \text{m}} = 2.51 \times 10^6 \, \text{mm} $

### Final Answers (Selected Parts for Conciseness)
1. A) $ \boldsymbol{4.5 \times 10^5} $; B) $ \boldsymbol{9.82 \times 10^{-6}} $; C) $ \boldsymbol{6.906 \times 10^0} $
2. A) $ \boldsymbol{4} $; B) $ \boldsymbol{2} $; C) $ \boldsymbol{3} $
3. A) $ \boldsymbol{18.8^\circ \text{C}} $; B) $ \boldsymbol{4.80 \, \text{g/mL}} $; C) $ \boldsymbol{0.00296 \, \text{km}} $
4. A) Calculator: $ \boldsymbol{8.38242} $, Rounded: $ \boldsymbol{8.4} $ (or $ 8.4 $ with 2 sig. figs); B) Calculator: $ \boldsymbol{2.294475} $, Rounded: $ \boldsymbol{2.29} $; C) Calculator: $ \boldsymbol{473.6} $, Rounded: $ \boldsymbol{470} $ (or $ 4.7 \times 10^2 $)
5. A) $ \boldsymbol{41.0 \, \text{cm}} $; B) $ \boldsymbol{0.0328 \, \text{L}} $; C) $ \boldsymbol{2.51 \times 10^6 \, \text{mm}} $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 1: Write each number in proper scientific notation

Part A: 450,000

Step 1: Move decimal to get \( 1 \leq a < 10 \)

Part B: 0.00000982

Step 1: Move decimal to get \( 1 \leq a < 10 \)

Part C: 6.906

Step 1: Check if \( 1 \leq a < 10 \)

Question 2: Determine significant figures

Part A: 17.30 mL

Answer:

Step 1: Conversion factors (\( 1 \, \text{km} = 1000 \, \text{m} \), \( 1 \, \text{m} = 1000 \, \text{mm} \))

Final Answers (Selected Parts for Conciseness)