Scientific Notation Calculator

Converting numbers to scientific notation

Scientific notation expresses any number as a coefficient between 1 and 10, multiplied by a power of 10. It's essential for working with very large numbers (like the distance to stars) or very small ones (like atomic measurements) without writing endless zeros.

The formula

a × 10^n where 1 ≤ |a| < 10 and n is an integer

To convert a standard number to scientific notation:

1. Move the decimal point until exactly one non-zero digit sits to its left
2. Count how many places you moved it—that's your exponent n
3. If you moved left (large number), n is positive; if right (small number), n is negative

To convert from scientific notation back to standard form, reverse the process: move the decimal point right for positive exponents, left for negative ones.

Worked example

Converting 45,620 to scientific notation:

Start: 45,620

Move the decimal point 4 places left to get 4.5620:

• 45,620 → 4.5620 × 10^4
• Simplified: 4.562 × 10^4

Verify: 4.562 × 10,000 = 45,620 ✓

Converting 0.000789 to scientific notation:

Start: 0.000789

Move the decimal point 4 places right to get 7.89:

• 0.000789 → 7.89 × 10^−4
• Result: 7.89 × 10^−4

Verify: 7.89 ÷ 10,000 = 0.000789 ✓

Converting 3.14 × 10^5 back to standard form:

The exponent is +5, so move the decimal 5 places right:

• 3.14000 → 314,000
• Result: 314,000

Converting 2.5 × 10^−3 back to standard form:

The exponent is −3, so move the decimal 3 places left:

• 0.0025
• Result: 0.0025

Common mistakes to avoid

Forgetting to adjust the exponent when simplifying the coefficient. If you write 45.62 × 10^3 instead of 4.562 × 10^4, the exponent is wrong. Always ensure your coefficient is between 1 and 10.

Confusing the sign of the exponent. Negative exponents represent small numbers (less than 1), not negative numbers. The number 3 × 10^−2 equals 0.03, which is positive.

Misplacing the decimal in the coefficient. The coefficient must have exactly one non-zero digit before the decimal point. 0.456 × 10^5 and 45.6 × 10^3 are both incorrect forms of 4.56 × 10^4.

Dropping trailing zeros incorrectly. While 4.562 × 10^4 and 4.5620 × 10^4 are mathematically equal, the number of significant figures matters in science. Keep trailing zeros if they reflect measurement precision.

This calculator handles all conversions automatically, so you can focus on understanding the concept rather than counting decimal places manually.