THE TRANSITION LINE // FIELD NOTES // STOP 22
Powers of ten and square roots
Field Book
Lessons 81 to 84
Method
Pencil and paper. Calculators never.
A lantern check under the trestle: finish under the bar before you climb out. The powers of ten ladder writes product notation compactly, multiplying by 100 percent over one converts any fraction, unit conversion runs metric and English lines, and square roots undo squaring with one standing rule: finish under the bar first.
What you have to be able to do
- Use powers of ten in product notation
- Change fractions to percents by the 100 percent move
- Convert within metric and English units
- Evaluate squares and square roots
The procedures
Powers of tenField Book Lesson 81
- 100 is 1, and each step up the ladder appends a zero.
- Product notation rides the ladder: each digit times its power of ten.
Percent by multiplyingField Book Lesson 82
- Multiply the fraction by 100%/1 and simplify.
- Mixed numbers go improper first, or cross by way of a decimal.
Metric and English conversionsField Book Lesson 83
- Convert one step at a time using the conversion facts.
- Going to a smaller unit multiplies. Going to a larger unit divides.
Squares and rootsField Book Lesson 84
- Squaring raises a number to the exponent 2. The square root asks which number squared gives this.
- The root of a sum is not the sum of roots: finish everything under the bar first.
Worked: finish under the bar
- √9 + 16 = √25 = 5
- while √9 + √16 = 3 + 4 = 7. Different answers, different claims.
Worked: up the ladder
- 4 · 103 = 4000
- and 26,000 = 2 · 104 + 6 · 103.
Terms on the record
| Term | Meaning |
|---|
| square root | the number that squares to the given number |
| power of ten | a rung on the tens ladder: 1, 10, 100, 1000, and on up |
| perfect square | a number that is some whole number squared |