Scientific Notation Calculator
Convert decimals, calculate with scientific notation, and learn powers of 10 with visual step-by-step solutions.
Background
Scientific notation writes very large or very small numbers as a coefficient multiplied by a power of 10. This calculator converts decimals, normalizes notation, performs operations, supports engineering notation, and explains every decimal shift visually.
How to use this calculator
- Choose decimal conversion, scientific notation conversion, normalization, operations, or engineering notation.
- Enter the number or coefficient and power of 10. Pasted forms like 3.2e5 and 3.2 × 10^5 are supported.
- Choose significant figures when rounding is needed.
- Click Calculate to see the answer, visual decimal shift, and step-by-step explanation.
Formula & Rules Used
Scientific notation: A × 10^n, where 1 ≤ |A| < 10.
Standard notation: the ordinary decimal form of the number, such as 320000.
Positive exponent: Move the decimal point right.
Negative exponent: Move the decimal point left.
Multiplication: Multiply coefficients and add powers of 10.
Division: Divide coefficients and subtract powers of 10.
Engineering notation: Use powers of 10 that are multiples of 3.
Example Problems & Step-by-Step Solutions
Example 1: Small decimal
Given: 0.00042
Step: Move the decimal 4 places right to get 4.2.
Answer: 4.2 × 10^-4.
Example 2: Large decimal
Given: 6020000
Step: Move the decimal 6 places left to get 6.02.
Answer: 6.02 × 10^6.
Example 3: Multiplication
Given: (3 × 10^4)(2 × 10^6)
Step: Multiply coefficients and add exponents: 3×2 = 6, 4+6 = 10.
Answer: 6 × 10^10.
Frequently Asked Questions
What is scientific notation?
Scientific notation writes a number as a coefficient multiplied by a power of 10, such as 4.2 × 10^-4.
What does the exponent mean?
A positive exponent moves the decimal right. A negative exponent moves the decimal left.
What is normalized scientific notation?
The coefficient should be at least 1 and less than 10 in absolute value, except for zero.
What is engineering notation?
Engineering notation is like scientific notation, but the exponent must be a multiple of 3.
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