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Math & School
Scientific Notation Calculator — Convert To & From a × 10^n
Turn huge and tiny numbers into clean a × 10^n form — and back again
Scientific notation is the compact way scientists, engineers and calculators write numbers that are very large or very small. Instead of dragging around a string of zeros, you write the number as a coefficient times a power of ten: a × 10^n, where the coefficient a satisfies 1 ≤ |a| < 10 and n is a whole-number exponent. The speed of light becomes 3 × 10^8 m/s instead of 300,000,000, and the mass of a proton becomes 1.6726 × 10⁻²⁷ kg instead of a number with 26 leading zeros.
The conversion rule is simple once you see it. To go to scientific notation, slide the decimal point until exactly one nonzero digit sits to its left, then count how far you moved it. Moving the point left (the number was large) gives a positive exponent; moving it right (the number was a small decimal) gives a negative exponent.
- 48,500 → move the point 4 places left → 4.85 × 10⁴
- 0.00072 → move the point 4 places right → 7.2 × 10⁻⁴
- −93,000,000 → keep the sign → −9.3 × 10⁷
To go back to standard form, do the reverse: a positive exponent shifts the decimal right (the number gets bigger), a negative exponent shifts it left (smaller). So 6.02 × 10²³ expands to 602,000,000,000,000,000,000,000.
There's a closely related format you'll see on calculators and in code: E-notation, where × 10^n is written as the letter E. 4.85 × 10⁴ becomes 4.85E4 (or 4.85e+04). It means exactly the same thing — the E just stands for "times ten to the."
This calculator does all of it in one place. Enter a plain number to get its proper scientific notation, the coefficient and exponent broken out, the E-notation form, and a note on engineering notation (a related style that restricts the exponent to multiples of 3, so the coefficient runs 1–999.99 and lines up with metric prefixes like kilo, mega, milli and micro). Or paste a value already in a × 10^n or E form and get the expanded standard decimal back. It handles negatives, leading zeros and a chosen number of significant figures, so you can check homework, read a datasheet, or tidy a spreadsheet export without counting zeros by hand.
Calculator
Fill in the fields and click "Calculate" for instant results.
📰 Formula
• Scientific notation form: a × 10^n, with 1 ≤ |a| < 10 and n an integer • To scientific: a = number ÷ 10^n, where n = number of places the decimal moved (left = +, right = −) • To standard: number = a × 10^n (positive n shifts the point right, negative n shifts it left) • E-notation: a × 10^n is written aEn (e.g. 4.85 × 10⁴ = 4.85E4) • Engineering notation: same value, but n is forced to a multiple of 3 so 1 ≤ |a| < 1000
📰 Formula
• Scientific notation form: a × 10^n, with 1 ≤ |a| < 10 and n an integer • To scientific: a = number ÷ 10^n, where n = number of places the decimal moved (left = +, right = −) • To standard: number = a × 10^n (positive n shifts the point right, negative n shifts it left) • E-notation: a × 10^n is written aEn (e.g. 4.85 × 10⁴ = 4.85E4) • Engineering notation: same value, but n is forced to a multiple of 3 so 1 ≤ |a| < 1000
🧪 Worked examples
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Example 2
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Example 3
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Example 4
⚠️ Common mistakes
- Leaving the coefficient outside 1 ≤ |a| < 10, like writing 48.5 × 10³ instead of 4.85 × 10⁴.
- Getting the exponent sign backwards — small decimals (< 1) need a negative exponent, not a positive one.
- Miscounting the decimal places moved, which throws the exponent off by one.
- Dropping the negative sign on a negative number when forming the coefficient.
- Confusing scientific notation (1 ≤ |a| < 10) with engineering notation (exponent a multiple of 3).
💡 Tips
- Count the decimal moves: left moves give a positive exponent, right moves give a negative one.
- The coefficient must have exactly one nonzero digit before the decimal point — that's the whole rule.
- E-notation (4.85E4) and a × 10^n are identical; the E just means '× 10 to the'.
- For engineering notation, round the exponent down to the nearest multiple of 3 so it lines up with kilo/mega/milli/micro.
- When multiplying numbers in scientific notation, multiply the coefficients and add the exponents.
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❓ Frequently asked questions
What is scientific notation?
Scientific notation writes a number as a coefficient times a power of ten, a × 10^n, where the coefficient is at least 1 and less than 10. It's a compact way to express very large or very small numbers without writing out long strings of zeros.
How do I convert a number to scientific notation?
Move the decimal point until exactly one nonzero digit is to its left, then count how many places you moved it. Moving left (a big number) gives a positive exponent; moving right (a small decimal) gives a negative exponent. Example: 48,500 = 4.85 × 10⁴.
How do I convert scientific notation back to a normal number?
Shift the decimal point by the exponent: a positive exponent moves it right (making the number larger), a negative exponent moves it left (smaller). So 7.2 × 10⁻⁴ becomes 0.00072 and 6.02 × 10²³ becomes a 24-digit number.
What does E or e mean in a number like 4.85E4 or 7.2e-4?
The E (or lowercase e) is E-notation, short for '× 10 to the power of.' So 4.85E4 means 4.85 × 10⁴ = 48,500, and 7.2e-4 means 7.2 × 10⁻⁴ = 0.00072. Calculators and programming languages use it because they can't display superscripts.
What's the difference between scientific and engineering notation?
Both are a × 10^n. Scientific notation keeps the coefficient between 1 and 10. Engineering notation forces the exponent to be a multiple of 3 (…, −3, 0, 3, 6, 9…), so the coefficient runs from 1 to just under 1000 and lines up with metric prefixes like kilo (10³), mega (10⁶), milli (10⁻³) and micro (10⁻⁶).
How do I handle negative numbers in scientific notation?
Keep the negative sign on the coefficient and form the notation from the absolute value. For example, −93,000,000 becomes −9.3 × 10⁷. The exponent only reflects the size of the number, never its sign.
Why is 10⁰ equal to 1, and what's the exponent for a number like 5?
Any nonzero number to the power of 0 equals 1, so 10⁰ = 1. A number already between 1 and 10, like 5, is written 5 × 10⁰ — the decimal didn't need to move, so the exponent is zero.
How do I multiply or divide numbers written in scientific notation?
To multiply, multiply the coefficients and add the exponents: (2 × 10³)(4 × 10²) = 8 × 10⁵. To divide, divide the coefficients and subtract the exponents. If the new coefficient falls outside 1–10, shift the decimal and adjust the exponent to renormalize.
How many significant figures should the coefficient have?
Match the precision of your data — typically 2 to 4 significant figures in the coefficient. Scientific notation makes significant figures explicit: 4.85 × 10⁴ clearly shows three significant figures, whereas 48,500 is ambiguous about trailing zeros.