Convert a number among scientific, E, engineering, and real-number notation, or calculate with coefficient-and-exponent values. Modes cover addition, subtraction, multiplication, division, powers, square roots, and squaring.
Examples
Convert 1,568,938
The scientific and E forms are 1.568938 × 10⁶ and 1.568938e6.
Add the default X and Y
1.23 × 10⁷ + 3.45 × 10² = 1.2300345 × 10⁷, or 12,300,345.
Formula
Scientific notation writes a nonzero number as b × 10^n, normally with
1 ≤ |b| < 10. Engineering notation instead requires n to be a multiple of 3.
Notation and precision
Scientific notation changes representation, not value: the coefficient is scaled while the exponent compensates. Displayed decimals may be rounded when the input exceeds JavaScript's reliable numeric precision. Preserve the original significant figures when notation is being used to communicate measurement precision.
Measurement and significant-figures activity
This original check-and-explain activity separates two skills that are often combined: rewriting a value in scientific notation and deciding how many digits a measurement should report. The calculator handles the notation and arithmetic. It does not know which digits were significant in the original measurement, so the student must make the final rounding decision.
Enter each value in Converter, record the scientific and engineering forms, then explain what changed and what stayed the same.
| Given value | Scientific notation | Engineering notation |
|---|---|---|
0.00000482 | 4.82 × 10^-6 | 4.82 × 10^-6 |
7.25e7 | 7.25 × 10^7 | 72.5 × 10^6 |
-0.00360 | -3.6 × 10^-3* | -3.6 × 10^-3* |
*The numeric converter does not preserve the written trailing zero in
-0.00360. In a measured quantity, that zero may communicate three
significant figures, so a student should write the converted result as
-3.60 × 10^-3 when the source measurement warrants it.
Next, use the Multiply mode for
(3.2 × 10^5) × (4.0 × 10^-3).
Student prompts
- What unrounded scientific-notation result does the calculator show?
- If both measurements have two significant figures, how should the final result be reported?
- Why is
72.5 × 10^6engineering notation but not normalized scientific notation? - Does moving the decimal point change the value of a number? Explain using the exponent.
Answer check
- The product is
1.28 × 10^3, or 1,280. - For the stated measurement rule, round to
1.3 × 10^3. The calculator exposes digits; it does not decide experimental precision. - Engineering notation uses an exponent divisible by three. Normalized
scientific notation instead keeps the coefficient at least 1 and less than
10, so the same value is
7.25 × 10^7. - No. Moving the decimal one place left is balanced by raising the power of ten by one, and moving it right is balanced by lowering the exponent.
Do not treat every displayed digit as measured precision. Significant-figure rules depend on the original observations and the operation being performed; the converter receives only numeric values, not measurement metadata.