1. **State the problem:** We need to find which number among 0.1245, 0.0255, 0.255, and 0.1255 rounds differently when rounded to two significant figures versus when rounded to two decimal places. 2. **Recall rounding rules:** - Rounding to two significant figures means keeping the first two non-zero digits and rounding the rest. - Rounding to two decimal places means keeping two digits after the decimal point and rounding the rest. 3. **Round each number to two significant figures:** - 0.1245: The first two significant figures are 1 and 2 (from 0.12), look at the next digit 4 (less than 5), so round down to 0.12. - 0.0255: The first two significant figures are 2 and 5 (from 0.025), next digit 5 means round up, so 0.026. - 0.255: The first two significant figures are 2 and 5 (from 0.25), next digit 5 means round up, so 0.26. - 0.1255: The first two significant figures are 1 and 2 (from 0.12), next digit 5 means round up, so 0.13. 4. **Round each number to two decimal places:** - 0.1245: Two decimal places means digits after decimal are 12, next digit 4 (less than 5), so 0.12. - 0.0255: Two decimal places means digits after decimal are 02, next digit 5 means round up, so 0.03. - 0.255: Two decimal places means digits after decimal are 25, next digit 5 means round up, so 0.26. - 0.1255: Two decimal places means digits after decimal are 12, next digit 5 means round up, so 0.13. 5. **Compare the results:** - 0.1245 rounds to 0.12 (sig figs) and 0.12 (decimal places) — same. - 0.0255 rounds to 0.026 (sig figs) and 0.03 (decimal places) — different. - 0.255 rounds to 0.26 (sig figs) and 0.26 (decimal places) — same. - 0.1255 rounds to 0.13 (sig figs) and 0.13 (decimal places) — same. **Final answer:** The number 0.0255 does not round to the same amount when rounded to two significant figures and two decimal places.