For AI agents: use /llms.txt for the Nakafa content index.
Physics often uses values that are too large or too small to write comfortably. An area of is still readable, but an electron mass of about makes it easy to lose count of the zeros.
Scientific notation writes a value as a coefficient multiplied by a power of .
For positive values, the standard form is:
The coefficient carries the significant figures. The exponent carries the scale.
The safest way to read scientific notation is to imagine moving the decimal point until the coefficient is between and .
| Ordinary value | Decimal movement | Scientific notation |
|---|---|---|
| places left | ||
| places right | ||
| places right |
If the decimal point moves left, the exponent is positive. If the decimal point moves right, the exponent is negative.
In scientific notation, the number of significant figures is read from the coefficient, not from the power of .
| Scientific notation | Significant figures | Reason |
|---|---|---|
| The coefficient is | ||
| The zero after the decimal point in is intentional | ||
| The coefficient is only | ||
| The zeros in express precision |
That is why scientific notation is useful for measurement. The value can be ambiguous, but clearly has significant figures.
When scientific notation is used for a measurement result, do not reverse the order.
For example, the calculated area of a bottle cap is . If the original diameter supports only significant figures, the area is written as:
Only after that do we convert the area to the International System of Units (SI). SI is the international measurement unit standard used in science.
So the SI scientific-notation result is .
Be careful with powered units. The conversion factor is powered too. From to , the factor is , but from to , the factor is .
Scientific notation also keeps operations tidy because powers of can be grouped.
Suppose a very small object has length and width .
The last step matters: the coefficient is not in standard form because it is not less than . We rewrite it as while preserving significant figures.
Measurement-value writing references from NIST Guide to the SI and OpenStax Significant Figures can be opened through the NIST link and
the OpenStax link.
