If a measured quantity is written correctly, which digits are certain?
seems like all but the last significant digit will be certain.
In order to determine which digits are certain in a measured quantity, you need to understand the concept of significant figures. Significant figures (also known as significant digits) are the digits in a number that carry meaning and contribute to the precision of the measurement.
Here are a few guidelines to determine which digits are considered certain or significant:
1. Non-zero digits (1-9) are always considered certain. For example, in the number 238.45, all digits (2, 3, 8, 4, and 5) are certain.
2. Zeroes between non-zero digits are also considered significant. For example, in the number 503, all three digits are significant.
3. Leading zeros (zeros before the first non-zero digit) are not considered significant. For example, in the number 0.025, the digits 2 and 5 are significant, while the leading zero is not.
4. Trailing zeros (zeros at the end of a number without a decimal point) may or may not be significant. It depends on whether the trailing zeros serve as placeholders or if they are measured. To indicate that the trailing zeros are significant, you can use scientific notation or add a decimal point at the end. For example, in the number 2000, the number of significant figures is ambiguous. However, if you write it as 2.000 x 10^3 or 2000., it indicates that all four digits are significant.
5. Trailing zeros after a decimal point are significant. For example, in the number 12.0, all three digits are significant.
In summary, the digits that are certain or significant in a measured quantity are all non-zero digits, zeros between non-zero digits, and trailing zeros after a decimal point (or indicated as significant through scientific notation or a decimal point at the end). Leading zeros are not considered significant unless they are part of a measurement.
Remember, properly expressing uncertainty and significant figures is crucial for clear communication in scientific measurements and calculations.