THE TRANSITION LINE // FIELD NOTES // STOP 20
Fraction to percent, exponents, and units
Field Book
Lessons 73 to 76
Method
Pencil and paper. Calculators never.
Room 5 opens this stop. Powers stack; units refuse to mix unconverted. A fraction turns percent through a bottom of 100 or a decimal bridge, exponents count repeated multiplication in three forms, perimeter extends to any closed shape, and time and distance units combine only after conversion.
What you have to be able to do
- Change fractions to percents
- Read and write the three exponential forms
- Find the perimeter of any straight-sided shape
- Combine and convert time and distance units
The procedures
Fraction to percentField Book Lesson 73
- Expand the bottom to 100 when it will go, and read the top as the percent.
- Otherwise ride the decimal bridge: fraction to decimal to percent.
ExponentsField Book Lesson 74
- The exponent tells how many times the base multiplies itself: exponential, product, and value forms.
- Memorize the squares through 102 and the cubes through 53.
Perimeter of any shapeField Book Lesson 75
- Add the lengths of all external edges, each exactly once.
Units of time and distanceField Book Lesson 76
- Same unit: combine the coefficients directly.
- Different units: convert everything to one unit first, then combine.
Worked: two powers
- 26 = 2 · 2 · 2 · 2 · 2 · 2 = 64
- 34 = 81
Worked: hours into minutes
- 2 hr + 35 min: convert first.
- 120 min + 35 min = 155 min
Terms on the record
| Term | Meaning |
|---|
| exponent | the count of times a base multiplies itself |
| base | the number an exponent acts on |
| exponential form | a base carrying an exponent |
| unit | the name of what is being counted or measured |