Scientific Notation Calculator
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Understanding Scientific Notation
What is Scientific Notation?
Scientific notation is a way to express very large or very small numbers in a compact form. It's written as a coefficient multiplied by a power of 10.
Standard Form
Converting to Scientific Notation
Large Numbers
Small Numbers
Operations with Scientific Notation
Multiplication
Division
Addition/Subtraction
Powers of 10 Reference
| Power | Prefix | Symbol | Name |
|---|---|---|---|
| 10¹² | tera | T | trillion |
| 10⁹ | giga | G | billion |
| 10⁶ | mega | M | million |
| 10³ | kilo | k | thousand |
| 10⁰ | one | ||
| 10⁻³ | milli | m | thousandth |
| 10⁻⁶ | micro | μ | millionth |
| 10⁻⁹ | nano | n | billionth |
| 10⁻¹² | pico | p | trillionth |
Famous Numbers in Scientific Notation
Physical Constants
- Speed of light: 2.998 × 10⁸ m/s
- Avogadro's: 6.022 × 10²³
- Planck's: 6.626 × 10⁻³⁴ J·s
- Electron mass: 9.109 × 10⁻³¹ kg
Astronomical Distances
- Earth-Sun: 1.496 × 10¹¹ m
- Light year: 9.461 × 10¹⁵ m
- Earth radius: 6.371 × 10⁶ m
- Moon distance: 3.844 × 10⁸ m
Common Homework Problems
Write 0.00056 in scientific notation
Step-by-Step Solution:
- Find the first non-zero digit: 5
- Place decimal after it: 5.6
- Count places moved right: 4 places (from 0.00056 to 5.6)
- Since we moved right, exponent is negative
Answer: 5.6 × 10⁻⁴
Write 123,000 in scientific notation
Step-by-Step Solution:
- Find the first non-zero digit: 1
- Place decimal after it: 1.23
- Count places moved left: 5 places (from 123000 to 1.23)
- Since we moved left, exponent is positive
Answer: 1.23 × 10⁵
Write 8.5 × 10⁴ in standard form
Step-by-Step Solution:
- Start with coefficient: 8.5
- Exponent is +4, so move decimal 4 places right
- Moving right: 8.5 → 85 → 850 → 8500 → 85000
- Add zeros as needed to fill places
Answer: 85,000
E Notation
Calculators and programming languages often use "E notation" where 3.2E8 means 3.2 × 10⁸. The "E" stands for "exponent." This notation is commonly seen in scientific software and programming languages like Python, JavaScript, and Excel.
Frequently Asked Questions
How do you convert a number to scientific notation?
Move the decimal point until you have one non-zero digit before it (1-9). Count how many places you moved - this is your exponent. If you moved left (large number), exponent is positive. If moved right (small number), exponent is negative. Example: 45,000 = 4.5 x 10 to the 4.
How do you multiply numbers in scientific notation?
Multiply the coefficients (the numbers in front) and add the exponents. Example: (3 x 10 to the 4) x (2 x 10 to the 5) = (3 x 2) x 10 to the (4+5) = 6 x 10 to the 9. If the coefficient becomes 10 or more, adjust by increasing the exponent.
What does E notation mean on a calculator?
E notation is shorthand for scientific notation on calculators and computers. 3.2E8 means 3.2 x 10 to the 8 (320,000,000). E-5 means 10 to the negative 5. This format is used because superscripts are hard to type on keyboards.
How do you add numbers in scientific notation?
First, make the exponents the same by adjusting one number. Then add the coefficients and keep the common exponent. Example: 3.2 x 10 to the 4 + 5.0 x 10 to the 3 = 3.2 x 10 to the 4 + 0.5 x 10 to the 4 = 3.7 x 10 to the 4.
How do you write 45000 in scientific notation step by step?
Step 1: Identify the first non-zero digit (4). Step 2: Place the decimal after it (4.5000). Step 3: Count how many places you moved the decimal left (4 places). Step 4: Write as coefficient times 10 raised to that power. Result: 45,000 = 4.5 × 10⁴. The exponent is positive because we moved the decimal left (the original number is greater than 10).