Lesson 1 of 13
Reading the Tape
Every error in this class that is not a thinking error is a reading error. This lesson is the foundation the other twelve stand on, and it is the one most people skip.
Step one
Read the material
Three ideas. The third one is the one that trips experienced men, because it looks like it should be obvious.
Concept one
What the marks actually mean
An inch on a standard tape is cut in half, then the halves in half, then again, then again. That gives you halves, quarters, eighths and sixteenths, and the marks get shorter as the fractions get smaller. The longest mark between the numbers is the half. The next longest are the quarters. The shortest are the sixteenths.
Count in sixteenths and reduce afterward. Eight sixteenths is a half. Twelve sixteenths is three quarters. Nobody writes 12/16 on a board, but counting to twelve is easier than trying to see three quarters directly, and it is how you avoid being one mark off.
One mark off is an eighth of an inch. On one cut nobody notices. On a stair with fourteen risers it is more than an inch and a half of accumulated error.
Concept two
Adding and subtracting without losing a sixteenth
To add two dimensions, put the fractions over the same denominator, add the fractions, add the inches, add the feet. Then clean up: if the fraction went over sixteen sixteenths, carry one inch. If the inches went over eleven, carry one foot.
Four foot seven and three eighths plus two foot nine and thirteen sixteenths. Three eighths is six sixteenths. Six plus thirteen is nineteen sixteenths, which is one and three sixteenths, so carry the inch. Seven plus nine plus that carried inch is seventeen, which is one foot five. Four plus two plus that carried foot is seven. Seven foot five and three sixteenths.
Slow the first ten times, automatic after that.
Concept three
Decimal feet, and why both systems are on the job
Your tape reads feet and inches. Your calculator, your laser, and most of the arithmetic in this class run in decimal feet. Surveyors and site plans use decimal feet almost exclusively. You will be handed both on the same job and expected to move between them.
To go from feet and inches to decimal feet, divide the inches by twelve and add. Nine foot four and a half is 4.5 divided by 12, which is 0.375, so 9.375 feet. To come back, take the decimal part and multiply by twelve. Point three seven five times twelve is four and a half inches.
The trap is people who round the decimal too early. Keep three decimal places until the last step. One thousandth of a foot is about a hundredth of an inch, and three decimals will always land you inside a sixteenth.
Step two
Work it with your hands on it
Slide the marker along the tape. The reading is computed from where it sits, in both systems, and the mark it is sitting on is named.
Hands on it, off the screen. Pull out a real tape. Have somebody call out a reading and mark it, or mark one and have them read it back. Do twenty of them.
Then measure something twice, once in feet and inches and once written as decimal feet, and check that you get the same board.
Step three
Prove you understood it
One question per idea, new numbers every time.
All three solid.
You can read a mark, add mixed dimensions without dropping a sixteenth, and move between feet-and-inches and decimal feet. Everything else in this class is built on that.
Trades Geometry
Lesson one of thirteen. Written by our founder, Dr. Gene A Constant, and donated to the Foundation. Published by Global Sovereign University Press.
The book page Buy a copy — it funds a free seatGSU is a 501(c)(3) nonprofit and book sales are its only income. A purchase is not a tax-deductible donation. As an Amazon Associate, GSU earns from qualifying purchases. This lesson is free and always will be.