How to Convert Decimal Numbers to Scientific Notation

July 14, 2026

The Three-Step Method

Converting any decimal number to scientific notation always follows the same three steps, whether the number is enormous or tiny. This guide walks through each step with worked examples, then hands off to the scientific notation calculator to check your work.

Step 1 — Find the decimal point’s new position. Move it so exactly one non-zero digit sits to its left.

Step 2 — Count the places moved. That count becomes the exponent.

Step 3 — Set the sign of the exponent. Moving left (number was 10 or more) gives a positive exponent. Moving right (number was less than 1) gives a negative exponent.

Example 1 — A Large Number

Convert 340,000 to scientific notation.

340,000 → 3.40000
Decimal moved 5 places to the left.
Result: 3.4 × 10⁵

Since the decimal moved left, the exponent is positive: 3.4 × 10⁵.

Example 2 — A Small Number

Convert 0.000521 to scientific notation.

0.000521 → 5.21
Decimal moved 4 places to the right.
Result: 5.21 × 10⁻⁴

Since the decimal moved right, the exponent is negative: 5.21 × 10⁻⁴.

Example 3 — A Negative Number

Convert -72,300 to scientific notation.

72,300 → 7.23
Decimal moved 4 places to the left.
Result: -7.23 × 10⁴

The negative sign carries through unchanged — it belongs to the mantissa, not the exponent. Only the size of the number (its magnitude) determines the exponent’s sign.

Example 4 — A Number Already Between 1 and 10

Convert 4.7 to scientific notation.

4.7 is already between 1 and 10 — the decimal doesn't need to move.
Result: 4.7 × 10⁰

Any number to the power of 0 equals 1, so 4.7 × 10⁰ = 4.7 × 1 = 4.7 — the conversion is valid even though the exponent is zero.

Converting to E Notation Instead

E notation follows the identical process — only the final formatting changes. Replace ”× 10” with the letter E: 3.4 × 10⁵ becomes 3.4E5, and 5.21 × 10⁻⁴ becomes 5.21E-4. See the notation glossary for the full distinction between scientific, E, and engineering notation.

Converting to Engineering Notation

Engineering notation uses the same three-step process, but Step 2’s target changes: instead of stopping at exactly one non-zero digit, keep moving until the exponent lands on a multiple of 3 (…-6, -3, 0, 3, 6…). For 340,000, moving the decimal 3 places (not 5) gives 340 × 10³ — still valid because the mantissa can range up to just under 1000 in engineering notation, and 3 is a multiple of 3.

Checking Your Work

A converted result is only correct scientific notation if the mantissa is between 1 and 10 (exclusive of 10 itself). If you land on something like 34 × 10⁴ or 0.34 × 10⁶, the decimal didn’t move far enough or moved too far — adjust the mantissa and exponent together until the mantissa falls in the 1–10 range. See common mistakes people make with scientific notation for the specific errors that trip this step up most often.

Practice With Real Numbers

Once the three-step method feels automatic, try it against real-world figures — distances in astronomy, masses in chemistry, file sizes in computing — in real-world examples of scientific notation. Then verify any conversion instantly with the scientific notation calculator, which shows scientific, E, and engineering notation side by side for the same input.