★ MATH · NOTATION · POWERS OF TEN
123,456 is 1.23456 × 10^5 — move the decimal point five places and the exponent counts the moves. Convert numbers to scientific notation and back, add, subtract, multiply and divide in scientific notation, or round to significant figures. This one is the SCIENTIFIC NOTATION tool — a × 10^b — the scientific-calculator page is the SCIENTIFIC tool — trig, logs and powers for single values — not notation; the significant-figures-calculator page is the SIGNIFICANT FIGURES tool — rounding to a count of digits — not conversion; and the decimal-to-fraction-converter page is the DECIMAL TO FRACTION tool — decimals as fractions — not powers of ten. No scientific notation calculator exists on this site — this one is the first.
Convert a number to scientific notation (a × 10^b, with 1 ≤ |a| < 10), convert it back, or do arithmetic in scientific notation. On the defaults it is 123,456, and the answer is 1.23456 × 10^5 — five places, exponent 5. Zero is 0 × 10^0 by convention, and a coefficient of 10 or more is normalised, not rejected.
It means 1.23456 multiplied by 10 five times — 1.23456 × 100,000, which is 123,456. The first part, 1.23456, is the coefficient: the number with the decimal point moved so exactly one non-zero digit sits to its left. The second part, 10^5, is the power of ten: the exponent 5 counts how many places the decimal point moved. Move it left and the exponent is positive; move it right and the exponent is negative. The form exists so very large and very small numbers stay readable: 987,654,321 is 9.87654321 × 10^8, and 0.00045 is 4.5 × 10^-4.
The coefficient must sit between 1 and 10. 12.3 × 10^4 is not scientific notation — it normalises to 1.23 × 10^5, because the coefficient 12.3 is too big and one more move of the decimal point fixes it. The calculator normalises any coefficient you type instead of complaining, and the exponent rises by one for every move.
Adding needs matching exponents; multiplying does not. To add 2.5 × 10^3 and 3.5 × 10^3 you add the coefficients, because the powers already agree — the answer is 6 × 10^3. To multiply 4 × 10^6 by 2 × 10^3 you multiply the coefficients (4 × 2 is 8) and add the exponents (6 + 3 is 9) — the answer is 8 × 10^9. Mixing the two rules up is the most common mistake in the chapter.
Zero is the one special case. Zero has no first non-zero digit, so there is nothing to put before the decimal point. By convention it is written 0 × 10^0 — the calculator states that plainly rather than failing on it.
On the defaults: 123456.
And the other way: 1.23456 × 10^5 means move the decimal point five places right — 123,456. And 4.5 × 10^-4 means move it four places left — 0.00045.
The defaults are the number 123456, chosen because it shows the whole method in one line: six digits, five moves, one exponent. They are a starting point, not a lesson: type any number — plain digits, a decimal point, or scientific form like 1.2e5 — and the calculator converts it, or switch the mode to add, subtract, multiply or divide two numbers in scientific notation, or to round a number to a chosen count of significant figures. The coefficient is always normalised to between 1 and 10, exponents are limited to ±308, and zero is 0 × 10^0 by convention.
These notes repeat in every explainer section because this page is built to be read start to finish: the coefficient must sit between 1 and 10; adding needs matching exponents and multiplying adds them; and zero is the one special case.
| Output | Formula | What it means |
|---|---|---|
| Number | input | 123,456. |
| Scientific notation | a × 10^b | 1.23456 × 10^5. |
| Scientific notation (6dp unrounded) | decimal, 6 places | 1.23456 × 10^5. |
| Exponent | count of moves | 5. |
| Formula | by mode | a × 10^b, with 1 ≤ |a| < 10. |
| Breakdown | step by step | 123,456 = 1.23456 × 10^5. |
| Verdict | in words | 123,456 is 1.23456 × 10^5. |
| Reverse: 1.23456 × 10^5 back to a plain number | step | 123456: 123,456 = 1.23456 × 10^5. |
| Reverse: 4.5 × 10^-4 back to a plain number | step | 0.00045: 0.00045 = 4.5 × 10^-4. |
| Reverse: 9.87654321 × 10^8 back to a plain number | step | 987654321: 987,654,321 = 9.87654321 × 10^8. |
| 0.00045 | same model | 0.00045 = 4.5 × 10^-4. |
| 7 | same model | 7 = 7 × 10^0. |
| 1,000,000 | same model | 1,000,000 = 1 × 10^6. |
| -0.0032 | same model | -0.0032 = -3.2 × 10^-3. |
| 0.5 | same model | 0.5 = 5 × 10^-1. |
| 987,654,321 | same model | 987,654,321 = 9.87654321 × 10^8. |
| (2.5 × 10^3) + (3.5 × 10^3) | same model | 2.5 × 10^3 + 3.5 × 10^3 = 6 × 10^3 (6,000). |
| (4 × 10^6) × (2 × 10^3) | same model | 4 × 10^6 × 2 × 10^3 = 8 × 10^9 (8,000,000,000). |
| (9 × 10^8) ÷ (3 × 10^4) | same model | 9 × 10^8 ÷ 3 × 10^4 = 3 × 10^4 (30,000). |
| (5 × 10^4) − (2 × 10^4) | same model | 5 × 10^4 − 2 × 10^4 = 3 × 10^4 (30,000). |
| 123456 to 3 significant figures | same model | 123,456 = 1.23 × 10^5. |
| Zero | same model | Zero has no first non-zero digit, so by convention it is 0 × 10^0.. |
| Non-numeric input | same model | Enter a number — digits, a decimal point, or scientific form like 1.2e5.. |
| Exponent out of range (|b| > 308) | same model | The exponent is out of range — keep it between −308 and 308.. |
| Coefficient 12.3 × 10^4 (|a| ≥ 10 — normalises) | same model | 123,000 = 1.23 × 10^5. |
Results are exact for the digits shown; displays round to 6 decimal places. The conversion itself is exact arithmetic on the number you typed — 123,456 is 1.23456 × 10^5 with nothing lost. JavaScript doubles lose integer precision beyond 2^53, so very large conversions are shown in scientific form only, and the plain-number display groups the digits with commas for reading. The calculator refuses non-numeric input and exponents beyond ±308, and it normalises coefficients of 10 or more instead of erroring. Significant-figures rounding follows the usual half-up rule: 123456 to 3 figures is 1.23 × 10^5.
123,456 is 1.23456 × 10^5 — move the decimal point 5 places and the exponent counts the moves. 0.00045 is 4.5 × 10^-4; 7 is 7 × 10^0; 1,000,000 is 1 × 10^6; -0.0032 is -3.2 × 10^-3; 0.5 is 5 × 10^-1; 987,654,321 is 9.87654321 × 10^8. (2.5 × 10^3) + (3.5 × 10^3) is 6 × 10^3; (4 × 10^6) × (2 × 10^3) is 8 × 10^9; (9 × 10^8) ÷ (3 × 10^4) is 3 × 10^4; (5 × 10^4) − (2 × 10^4) is 3 × 10^4. 123456 to 3 significant figures is 1.23 × 10^5. 1.23456 × 10^5 back to a plain number: 123456. 4.5 × 10^-4 back to a plain number: 0.00045. 9.87654321 × 10^8 back to a plain number: 987654321. Source: Bright Side Kit, brightoolbox.com.
123,456 is 1.23456 × 10^5 — move the decimal point five places and the exponent counts the moves. Put the decimal point after the first non-zero digit, count the places it moved, and that count is the exponent.
0.00045 is 4.5 × 10^-4. Move the decimal point four places to the right to reach 4.5, so the exponent is -4 — small numbers get negative exponents.
Make the exponents match, then add the coefficients — (2.5 × 10^3) + (3.5 × 10^3) is 6 × 10^3. If the exponents differ, shift one number until they agree, then add.
Multiply the coefficients and add the exponents — (4 × 10^6) × (2 × 10^3) is 8 × 10^9. For division, divide the coefficients and subtract the exponents: (9 × 10^8) ÷ (3 × 10^4) is 3 × 10^4.
123456 to 3 significant figures is 1.23 × 10^5. Keep three digits and let the exponent carry the size — the answer is not 123,000 rounded, it is 1.23 × 10^5.
Move the decimal point by the exponent — 1.23456 × 10^5 is 123,456, and 4.5 × 10^-4 is 0.00045. A positive exponent moves the point right, a negative one moves it left.
Zero is 0 × 10^0 by convention. It has no first non-zero digit, so there is nothing to put before the decimal point — the calculator states the convention instead of failing.
Because the coefficient must be between 1 and 10 — 12.3 × 10^4 normalises to 1.23 × 10^5. Move the decimal point one more place left and the exponent rises by one.