Unit Conversion and Scientific Notation Worksheet for practicing metric unit conversions, comparisons, and scientific notation.

Let's solve each part of the Unit Conversion and Scientific Notation Worksheet step by step.

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A. Convert the following numbers to the units located to the right of the blank.

We'll use standard metric conversions:

- Length:
- 1 m = 100 cm = 1000 mm
- 1 mm = 1000 μm (micrometers)
- 1 pm = 10⁻¹² m

- Mass:
- 1 kg = 1000 g = 1,000,000 mg = 1,000,000,000 μg
- 1 mg = 1000 μg
- 1 pg = 10⁻¹² g

- Volume:
- 1 L = 1000 mL = 10 dL
- 1 mL = 1000 μL

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#### A. Conversions

1. 109 mm = ______ cm
$ 109 \div 10 = 10.9 $ cm
→ 10.9 cm

2. 58 g = ______ kg
$ 58 \div 1000 = 0.058 $ kg
→ 0.058 kg

3. 0.813 kg = ______ mg
$ 0.813 \times 1000 = 813 $ g → $ 813 \times 1000 = 813,000 $ mg
→ 813,000 mg

4. 4.7 cm = ______ mm
$ 4.7 \times 10 = 47 $ mm
→ 47 mm

5. 220 μg = ______ kg
$ 220 \mu g = 220 \times 10^{-6} g = 2.2 \times 10^{-4} g $
$ 2.2 \times 10^{-4} g = 2.2 \times 10^{-7} kg $
→ 2.2 × 10⁻⁷ kg

6. 0.571 L = ______ mL
$ 0.571 \times 1000 = 571 $ mL
→ 571 mL

7. 5.86 μL = ______ mL
$ 5.86 \div 1000 = 0.00586 $ mL
→ 0.00586 mL

8. 49.8 g = ______ mg
$ 49.8 \times 1000 = 49,800 $ mg
→ 49,800 mg

9. 743 mL = ______ L
$ 743 \div 1000 = 0.743 $ L
→ 0.743 L

10. 110 μg = ______ mg
$ 110 \div 1000 = 0.110 $ mg
→ 0.110 mg

11. 4,279 pg = ______ mg
$ 4,279 \text{ pg} = 4.279 \times 10^{-12} g $
$ = 4.279 \times 10^{-9} mg $
→ 4.279 × 10⁻⁹ mg

12. 5.1 L = ______ mL
$ 5.1 \times 1000 = 5,100 $ mL
→ 5,100 mL

13. 10 mm = ______ cm
$ 10 \div 10 = 1 $ cm
→ 1 cm

14. 300 mL = ______ dL
$ 300 \div 100 = 3 $ dL
→ 3 dL

15. 1005 μL = ______ L
$ 1005 \div 1,000,000 = 0.001005 $ L
→ 0.001005 L

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B. Compare the following calculations using >, <, or =

Convert both sides to same unit and compare.

1. 50 cm ___ 5 m
50 cm = 0.5 m → 0.5 m < 5 m
→ <

2. 2.6 L ___ 260 mL
2.6 L = 2600 mL → 2600 mL > 260 mL
→ >

3. 430 mm ___ 0.43 m
430 mm = 0.43 m → equal
→ =

4. 0.5 kg ___ 50 g
0.5 kg = 500 g → 500 g > 50 g
→ >

5. 0.65 mL ___ 650 μL
0.65 mL = 650 μL → equal
→ =

6. 0.70 g ___ 0.70 mg
0.70 g = 700 mg → 700 mg > 0.70 mg
→ >

7. 89 mL ___ 0.89 L
89 mL = 0.089 L → 0.089 L < 0.89 L
→ <

8. 10 m ___ 1000 cm
10 m = 1000 cm → equal
→ =

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C. Express the following numbers in scientific notation

Scientific notation: $ a \times 10^n $, where $ 1 \leq a < 10 $

1. 3000 kg
$ 3 \times 10^3 $ kg

2. 0.00375 cm
Move decimal 3 places right → $ 3.75 \times 10^{-3} $ cm

3. 0.421 m
$ 4.21 \times 10^{-1} $ m

4. 5005 g
$ 5.005 \times 10^3 $ g

5. 7,008,000 μL
$ 7.008 \times 10^6 $ μL

6. 890 g
$ 8.9 \times 10^2 $ g

7. 0.4039 L
$ 4.039 \times 10^{-1} $ L

8. 0.1007 pm
$ 1.007 \times 10^{-1} $ pm

9. 200 L
$ 2 \times 10^2 $ L

10. 0.987 mm
$ 9.87 \times 10^{-1} $ mm

11. 12.8 kg
$ 1.28 \times 10^1 $ kg

12. 120 m
$ 1.2 \times 10^2 $ m

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✔ Final Answers:

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#### A. Conversions

1. 10.9 cm
2. 0.058 kg
3. 813,000 mg
4. 47 mm
5. 2.2 × 10⁻⁷ kg
6. 571 mL
7. 0.00586 mL
8. 49,800 mg
9. 0.743 L
10. 0.110 mg
11. 4.279 × 10⁻⁹ mg
12. 5,100 mL
13. 1 cm
14. 3 dL
15. 0.001005 L

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#### B. Comparisons

1. <
2. >
3. =
4. >
5. =
6. >
7. <
8. =

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#### C. Scientific Notation

1. $ 3 \times 10^3 $ kg
2. $ 3.75 \times 10^{-3} $ cm
3. $ 4.21 \times 10^{-1} $ m
4. $ 5.005 \times 10^3 $ g
5. $ 7.008 \times 10^6 $ μL
6. $ 8.9 \times 10^2 $ g
7. $ 4.039 \times 10^{-1} $ L
8. $ 1.007 \times 10^{-1} $ pm
9. $ 2 \times 10^2 $ L
10. $ 9.87 \times 10^{-1} $ mm
11. $ 1.28 \times 10^1 $ kg
12. $ 1.2 \times 10^2 $ m

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