How to Find 5 8th of an Inch on a Ruler

In the world of rulers and measurements, there is often confusion about the exact meaning of fractional notations. The phrase “5 8th of an inch” may sound like a measurement in feet-and-inches notation (i.e., 5’ 8”), but that’s actually incorrect. Five-eighths of one inch is different from five feet eight inches.

Find 5 8th of an inch on an eighth-inch scale

On an eighth-inch scale, there are eight equal intervals between each whole inch. Each interval represents a fraction of the total length: zero graduation is the starting point of the ruler, and it is excluded from the count. Five intervals from zero equals the fifth eighth-inch position. You can find this point by counting up the increments to locate the fifth eighth-inch mark. However, you should also look at the neighboring fractions: half-inch (4/8) and three-quarters (6/8). In this case, the 5/8 increment is located halfway between 1/2 and 3/4 inch. On a documented scale, these increments appear as lines; the half-inch line will be shorter than the whole-inch lines, and the quarter-inch lines will be next longest. The eighth-inch increments are created by splitting the quarter-inch lines into two parts, or by marking off each quarter inch as two intervals. This gives us the eighth-inch increments.

The same location appears on a finer scale using equivalent fractions. Again, you’ll want to count the number of equal intervals between the graduations and locate the correct tick mark. If we use a 16th-inch scale, the markings represent 16 equal intervals per inch, which is just double the eighth-inch scale. In this case, five-eighths of an inch is equal to 10/16. You’ll need to count ten sixteenth-inch intervals from zero, which would place you at the tenth sixteenth-inch increment. You’d stop at that graduation. Because the eighth sixteenth-inch tick is exactly 1/2 inch, your calculation should include the distance from zero to 1/2 inch (eight intervals), plus the two sixteenth-inch intervals beyond that (a total of ten). On a documented scale, the smallest lines usually mark 1/16 inch, so they’re the shortest ticks.

Exact equivalents in inches millimeters and centimeters

Five eighths of an inch is approximately 0.625 inch, with the exact value being 5 ÷ 8 = 0.625. A single inch measures exactly 25.4 millimeters. So 0.625 × 25.4 = exactly 15.875 millimeters. Since 10 millimeters equals 1 centimeter, 15.875 millimeters equals exactly 1.5875 centimeters. All of these are exact arithmetic equivalents, but they don’t determine how accurately you can read any particular physical ruler.

Sources

• What is 5' 8" in Inches? - Inch Calculator
• SI Units – Length | NIST
• Inch - Wikipedia
• How to Read a Tape Measure