Scientific Notation Practice Worksheet
Mathematics & Science 20 Applied Exercises • Part 1
Scientific Notation Practice
Name:
Date: Period:
Standard Form: \( a \times 10^b \) where \( 1 \le |a| < 10 \) and \( b \) is an integer.
Move left: \( +b \) (large #) • Move right: \( -b \) (small decimal)
Part 1: Convert Standard Measurements to Scientific Notation
Double-spaced work lines for decimal counting
1 Earth-Moon Distance
384,400 km
Work / decimal shifts:
Answer:
2 Stars in Milky Way
100,000,000,000
Work / decimal shifts:
Answer:
3 Speed of Light
299,800,000 m/s
Work / decimal shifts:
Answer:
4 Age of Earth
4,540,000,000 years
Work / decimal shifts:
Answer:
5 Blue Whale Mass
190,000 kg
Work / decimal shifts:
Answer:
6 Red Blood Cell Width
0.0000075 m
Work / decimal shifts:
Answer:
7 DNA Strand Width
0.000000002 m
Work / decimal shifts:
Answer:
8 Violet Light Wavelength
0.0000004 m
Work / decimal shifts:
Answer:
9 Flu Virus Diameter
0.00000012 m
Work / decimal shifts:
Answer:
10 Fine Dust Particle Mass
0.000000053 g
Work / decimal shifts:
Answer:
Exercises 1–10 • Standard to Scientific Form Turn over for Part 2 & Applications (Exercises 11–20) →
Mathematics & Science Part 2 • Expansion & Applications
Expanding Scientific Notation
Name:
Date:
Decimal Movement: \( 10^{+n} \rightarrow \) shift right \( n \) places; \( 10^{-n} \rightarrow \) shift left \( n \) places.
Fill vacant spaces with zeros
Part 2: Convert to Standard Notation & Solve Real-World Cases
Double-spaced work areas for scratch calculations
11 Global Human Population
\( 8.05 \times 10^9 \) people
Work / decimal shifts:
Standard Form:
12 Hydrogen Atom Radius
\( 5.29 \times 10^{-11} \) m
Work / decimal shifts:
Standard Form:
13 Cloud Data Transferred
\( 3.4 \times 10^{12} \) gigabytes
Work / decimal shifts:
Standard Form:
14 Light Travel Time (1 ft)
\( 1.02 \times 10^{-9} \) seconds
Work / decimal shifts:
Standard Form:
15 Solar Core Temperature
\( 1.57 \times 10^7 \) Kelvin
Work / decimal shifts:
Standard Form:
16 Microchip Gate Length
\( 3.0 \times 10^{-9} \) m
Work / decimal shifts:
Standard Form:
17 Orbit of Jupiter
\( 7.78 \times 10^8 \) km from Sun
Work / decimal shifts:
Standard Form:
18 Colony Doubling
Double: \( 1.6 \times 10^5 \) bacteria
Work / multiply by 2:
New Total:
19 Oceans Water Volume
\( 1.386 \times 10^9\text{ km}^3 \) water
Work / decimal shifts:
Standard Form:
20 Amoeba Cell Length
\( 5.0 \times 10^{-4} \) m
Work / decimal shifts:
Standard Form:
Exercises 11–20 • Scientific to Standard Form & Applied Cases Completed Practice Worksheet
Scientific Notation Answer Key
Teacher Resource Complete Worked Solutions
Scientific Notation Answer Key
All 20 Exercises Parts 1 & 2 • Complete Key
Grading Guide: Ensure the coefficient \( 1 \le |a| < 10 \) and powers of 10 match sign and magnitude.
Full credit for correct decimal shift steps
Part 1: Standard to Scientific (1–10) \( a \times 10^b \)
1. Earth-Moon Distance 384,400 km
Shift 5 places left (\( +5 \)) \( 3.844 \times 10^5\text{ km} \)
2. Stars in Milky Way 100,000,000,000
Shift 11 places left (\( +11 \)) \( 1.0 \times 10^{11} \)
3. Speed of Light 299,800,000 m/s
Shift 8 places left (\( +8 \)) \( 2.998 \times 10^8\text{ m/s} \)
4. Age of Earth 4,540,000,000 yrs
Shift 9 places left (\( +9 \)) \( 4.54 \times 10^9\text{ yrs} \)
5. Blue Whale Mass 190,000 kg
Shift 5 places left (\( +5 \)) \( 1.9 \times 10^5\text{ kg} \)
6. Red Blood Cell Width 0.0000075 m
Shift 6 places right (\( -6 \)) \( 7.5 \times 10^{-6}\text{ m} \)
7. DNA Strand Width 0.000000002 m
Shift 9 places right (\( -9 \)) \( 2.0 \times 10^{-9}\text{ m} \)
8. Violet Light Wavelength 0.0000004 m
Shift 7 places right (\( -7 \)) \( 4.0 \times 10^{-7}\text{ m} \)
9. Flu Virus Diameter 0.00000012 m
Shift 7 places right (\( -7 \)) \( 1.2 \times 10^{-7}\text{ m} \)
10. Dust Particle Mass 0.000000053 g
Shift 8 places right (\( -8 \)) \( 5.3 \times 10^{-8}\text{ g} \)
Part 2: Scientific to Standard (11–20) Expanded Form
11. Global Population \( 8.05 \times 10^9 \)
Shift 9 places right 8,050,000,000 people
12. Hydrogen Atom Radius \( 5.29 \times 10^{-11} \)
Shift 11 places left 0.0000000000529 m
13. Cloud Data Transferred \( 3.4 \times 10^{12} \)
Shift 12 places right 3,400,000,000,000 GB
14. Light Travel Time (1 ft) \( 1.02 \times 10^{-9} \)
Shift 9 places left 0.00000000102 s
15. Sun Core Temp \( 1.57 \times 10^7 \)
Shift 7 places right 15,700,000 K
16. Microchip Gate Length \( 3.0 \times 10^{-9} \)
Shift 9 places left 0.000000003 m
17. Orbit of Jupiter \( 7.78 \times 10^8\text{ km} \)
Shift 8 places right 778,000,000 km
18. Colony Doubling Double \( 1.6 \times 10^5 \)
\( 2 \times 1.6 \times 10^5 \) \( 3.2 \times 10^5\text{ bacteria} \)
19. Ocean Water Volume \( 1.386 \times 10^9\text{ km}^3 \)
