1. The problem asks to find the length shown on the micrometer in inches. 2. A micrometer reading is found by adding the main scale reading to the thimble scale reading. 3. The main scale reading is the number of whole divisions visible on the sleeve. Here, the sleeve shows 5 full divisions, so the main scale reading is $5$. 4. The thimble scale reading is the number on the rotary scale that aligns with the horizontal line on the sleeve. Here, the rotary scale shows $6$. 5. Each division on the thimble scale represents $0.001$ inches. 6. Therefore, the thimble reading is $6 \times 0.001 = 0.006$ inches. 7. Add the main scale and thimble readings: $$5 + 0.006 = 5.006$$ inches. 8. The length shown on the micrometer is $5.006$ inches.