Accepted answer
Answer included
Counting the 110. sig fig
The number 110. (with a trailing decimal point) contains three significant figures. The decimal point communicates that the measurement is written to the ones place, so the trailing zero is intentional and significant.
Key rule (trailing zeros):
Trailing zeros are significant only if a decimal point is shown (or the number is written in scientific
notation that makes the significance explicit).
Step-by-step reasoning
- Identify the digits: 1, 1, and 0.
- Apply the nonzero-digit rule: all nonzero digits are significant, so both 1s are significant.
- Apply the trailing-zero rule using the decimal point: in 110., the decimal point indicates the zero is a measured (reported) digit, so the 0 is significant.
- Count significant digits: \(2 + 1 = 3\), so 110. has \(3\) significant figures.
Scientific notation check
Writing 110. in scientific notation makes the significance explicit: \[110. = 1.10 \times 10^2\] The coefficient 1.10 shows three significant digits (the trailing zero after the decimal is significant).
Common related cases
| Number | Significant figures | Reason (sig fig rule) |
|---|---|---|
| 110. | 3 | Decimal point indicates the trailing zero is significant. |
| 110 | Usually 2 (context-dependent) | Trailing zero without a decimal point is commonly treated as not significant unless specified. |
| 110.0 | 4 | All digits including the trailing zero after the decimal are significant. |
| 0.0110 | 3 | Leading zeros are not significant; the trailing zero after the decimal is significant. |
| \(1.10 \times 10^2\) | 3 | Scientific notation explicitly shows the significant digits in the coefficient. |
Conclusion
For significant figures (sig figs), 110. has three significant figures because the decimal point indicates that the trailing zero is a meaningful, measured digit rather than a placeholder.
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