Example of Scientific Notation
Scientific notation is a method of writing very large or very small numbers using powers of 10. An example of scientific notation is \( 6.02 \times 10^{23} \), which represents Avogadro's number (602,000,000,000,000,000,000,000). This format makes it easier to work with extreme values common in science, mathematics, and engineering.
Standard Scientific Notation Examples
Large Number: \( 5.8 \times 10^9 \) = 5,800,000,000
Small Number: \( 3.7 \times 10^{-5} \) = 0.000037
Speed of Light: \( 3.0 \times 10^8 \) m/s = 300,000,000 m/s
Planck's Constant: \( 6.626 \times 10^{-34} \) J·s
Adding Scientific Notation Examples
Rule for Adding Scientific Notation:
The exponents must be the SAME before you can add the coefficients!
Example 1: Same Exponents
Adding \( (4.5 \times 10^6) + (2.3 \times 10^6) \)
Step 1: Check exponents → Both are \( 10^6 \) ✓
Step 2: Add coefficients → \( 4.5 + 2.3 = 6.8 \)
Step 3: Keep the exponent → \( 10^6 \)
Answer: \( 6.8 \times 10^6 \)
Example 2: Different Exponents
Adding \( (5.0 \times 10^7) + (3.0 \times 10^5) \)
Step 1: Exponents are different (7 and 5) → Must adjust!
Step 2: Convert to same exponent. Rewrite \( 3.0 \times 10^5 \) as \( 0.03 \times 10^7 \)
Step 3: Now add → \( (5.0 + 0.03) \times 10^7 = 5.03 \times 10^7 \)
Answer: \( 5.03 \times 10^7 \)
Example 3: With Negative Exponents
Adding \( (7.5 \times 10^{-3}) + (2.1 \times 10^{-3}) \)
Step 1: Same exponents (\( 10^{-3} \)) ✓
Step 2: Add coefficients → \( 7.5 + 2.1 = 9.6 \)
Answer: \( 9.6 \times 10^{-3} \)
Decimal Notation Example
Decimal notation is the standard way of writing numbers without exponents.
Examples of Decimal Notation
Example 1: 456.789 (already in decimal notation)
Example 2: 0.00025 (decimal with leading zeros)
Example 3: 12,500,000 (large decimal number)
Conversion: \( 3.45 \times 10^4 \) = 34,500 (decimal notation)
Example of Standard Notation
Standard notation is another term for regular decimal notation—the everyday way we write numbers.
Standard Notation Examples
Population: 8,000,000,000 (eight billion)
Distance: 384,400 km (Earth to Moon)
Microscopic: 0.0000001 meters (100 nanometers)
From Scientific: \( 5.67 \times 10^3 \) = 5,670 (standard notation)
Exponential Notation Example
Exponential notation uses exponents to express repeated multiplication or powers of 10.
Exponential Notation Examples
Powers of 2: \( 2^8 = 256 \)
Powers of 10: \( 10^5 = 100,000 \)
Scientific Form: \( 6.022 \times 10^{23} \) (Avogadro's number)
Negative Exponent: \( 10^{-6} = 0.000001 \)
Frequently Asked Questions
What is an example of scientific notation?
An example of scientific notation is \( 6.02 \times 10^{23} \), which represents Avogadro's number (602,000,000,000,000,000,000,000). Another example is \( 3.0 \times 10^8 \) for the speed of light in meters per second. Scientific notation consists of a coefficient between 1-10 multiplied by a power of 10.
How do you add numbers in scientific notation?
To add in scientific notation, follow these adding scientific notation examples: (1) Make sure exponents are the same, (2) Add the coefficients, (3) Keep the exponent. Example: \( (4 \times 10^5) + (3 \times 10^5) = 7 \times 10^5 \). If exponents differ, adjust one number first.
What is a decimal notation example?
A decimal notation example is 345,000 or 0.00067—regular numbers without exponents. These are the everyday way we write numbers. Converting from scientific notation: \( 3.45 \times 10^5 \) becomes 345,000 in decimal notation. Decimal notation shows the full value with all digits visible.
What is an example of standard notation?
An example of standard notation is 7,850,000 or 0.00032—the normal way of writing numbers. Standard notation is the same as decimal notation. It's the opposite of scientific notation. For instance, \( 5.6 \times 10^4 \) in standard notation is 56,000.
What is an exponential notation example?
An exponential notation example is \( 2^8 = 256 \) or \( 10^6 = 1,000,000 \). Exponential notation uses exponents to show repeated multiplication. In scientific notation, \( 5.3 \times 10^7 \) uses exponential notation for the power of 10. It's a compact way to express large or small numbers.
What are real life examples of scientific notation?
Real life examples of scientific notation include: Earth's population (\( 8 \times 10^9 \)), distance to the Moon (\( 3.844 \times 10^8 \) m), mass of an electron (\( 9.109 \times 10^{-31} \) kg), number of cells in the human body (\( 3.7 \times 10^{13} \)), and computer processing speeds (\( 10^{15} \) operations/second).
What are good scientific notation project examples?
Scientific notation project examples include: creating a "Powers of 10" poster showing scale from atoms to universe, making a solar system distance model with scientific notation labels, collecting news articles and converting numbers to scientific notation, creating a microscopic-to-cosmic booklet, or designing an infographic comparing magnitudes of different phenomena.
Why do scientists use scientific notation?
Scientists use scientific notation because it makes very large numbers (like \( 6.02 \times 10^{23} \) atoms) and very small numbers (like \( 1.6 \times 10^{-19} \) coulombs) easier to write, read, and calculate with. It also clearly shows significant figures and simplifies multiplication and division of extreme values common in physics, chemistry, and astronomy.
How do you know when to use scientific notation?
Use scientific notation when: (1) Numbers are very large (≥1,000,000) or very small (≤0.001), (2) Working with scientific data, (3) Performing calculations that would be cumbersome in standard form, (4) Showing significant figures clearly, (5) Comparing orders of magnitude. Examples: astronomy, chemistry, microbiology, and nanotechnology all routinely use it.
Can you give an example of adding scientific notation with different exponents?
Example: Add \( (6 \times 10^7) + (4 \times 10^5) \). Step 1: Convert to same exponent—rewrite \( 4 \times 10^5 \) as \( 0.04 \times 10^7 \). Step 2: Add coefficients—\( 6 + 0.04 = 6.04 \). Step 3: Result is \( 6.04 \times 10^7 \). This is a common adding scientific notation example.
