Scientific Notation Calculator
Convert any number to scientific notation or standard form.
About This Calculator
Convert any number to scientific notation or standard form. Use the calculator above for instant results.
How Scientific Notation Represents Scale
Scientific notation separates a number into a coefficient that carries the significant digits and a power of ten that carries the scale. In normalized scientific notation, a nonzero decimal number is written as a × 10n, where 1 ≤ |a| < 10 and n is an integer.
Moving the decimal point left makes the coefficient smaller, so the power of ten must increase to preserve the value. Moving it right makes the coefficient larger, so the exponent decreases. For 6,700,000,000, the decimal moves nine places left to produce 6.7, giving 6.7 × 109. For 0.000045, it moves five places right to produce 4.5, giving 4.5 × 10−5.
The sign of the original number belongs to the coefficient; it does not determine the sign of the exponent. A negative exponent means the magnitude is less than 1, while a negative coefficient means the number itself is below zero. Zero is a special case because there is no unique normalized exponent for it, so it is normally written as 0 rather than 0 × 10n.
Scientific notation is especially useful for comparing orders of magnitude and for arithmetic. Multiplication combines coefficients and adds exponents; division divides coefficients and subtracts exponents. Addition and subtraction require matching powers of ten first, because coefficients can be directly combined only when they refer to the same place-value scale.
Worked Examples
- 4.5 x 10^-5
Answer: 4.5 x 10^-5
- 6.7 x 10^9
Answer: 6.7 x 10^9
- 1 x 10^-3
Answer: 1 x 10^-3
Convert 0.00000072.
- Move the decimal 7 places right: 7.2
- The movement to the right gives exponent −7.
Answer: 7.2 × 10−7
The negative exponent describes a magnitude much smaller than one.
Convert −3,450,000.
- Move the decimal 6 places left while keeping the negative sign.
Answer: −3.45 × 106
The exponent is positive because the magnitude is large; the coefficient is negative because the original number is negative.
Who Uses This Calculator?
Large and small numbers.
Engineering notation.
Teach scientific notation.
Floating point representation.
Common Mistakes to Avoid
❌ Coefficient must be 1-10
In proper scientific notation, coefficient is >= 1 and < 10. 45x10^3 is wrong; 4.5x10^4 is correct.
❌ E notation confusion
4.5e-5 means 4.5 x 10^-5, not 4.5 x e^-5.
❌ Using a coefficient such as 45 or 0.45
Normalized scientific notation requires the coefficient magnitude to be at least 1 and less than 10. Rewrite 45 × 103 as 4.5 × 104.
❌ Adding coefficients before matching exponents
For 3 × 105 + 4 × 104, first rewrite the second term as 0.4 × 105. The sum is 3.4 × 105, not 7 × 109.
Frequently Asked Questions
Scientific notation format?
a x 10^n where 1 <= |a| < 10.
Why use it?
Avoids writing many zeros. Makes multiplication/division easier.
Multiplying in SN?
Multiply coefficients, add exponents: (3x10^2)(4x10^3) = 12x10^5 = 1.2x10^6.
What does a negative exponent mean?
A negative exponent means the power of ten is a reciprocal. For example, 10−3 = 1/1000 = 0.001. Therefore 4.2 × 10−3 equals 0.0042.
How do I compare two numbers in scientific notation?
Compare exponents first when both coefficients are normalized and positive. The larger exponent has the larger magnitude. If the exponents match, compare coefficients. For negative numbers, remember that the ordering reverses with magnitude.
Is engineering notation the same as scientific notation?
No. Engineering notation restricts the exponent to multiples of three, which aligns with SI prefixes such as kilo, mega, milli, and micro. Its coefficient may range from 1 up to less than 1000.
How are significant figures preserved?
The coefficient carries the significant figures. Writing 6.70 × 104 communicates three significant figures, whereas 6.7 × 104 communicates two when trailing zeros are being used to show measured precision.
Formula Explorer connections
Interpretation: This relationship converts, summarizes or checks numerical quantities using standard arithmetic and measurement rules. Assumption: Use consistent units, preserve enough significant digits, and round only the final result unless the method states otherwise.