THE TRANSITION LINE // FIELD NOTES // STOP 19
Fractions to decimals to percents, both directions
Field Book
Lessons 69 to 72
Method
Pencil and paper. Calculators never.
Second leg of the Line. The exchange window reopens at full speed. A fraction becomes a decimal by expanding its bottom to a power of ten or by dividing it out, fractions compare over one bottom or in decimal form, complementary fractions add to one, and a decimal becomes a percent with a two-place move.
What you have to be able to do
- Change fractions to decimals both ways
- Compare fractions
- Name the complement of a fraction
- Change decimals and whole numbers to percents
The procedures
Fraction to decimalField Book Lesson 69
- When the bottom will expand to 10, 100, or 1000, expand it and read the places.
- Otherwise divide top by bottom, adding zeros. A digit that repeats takes the bar.
Comparing fractionsField Book Lesson 70
- Expand both fractions to the same bottom and compare tops.
- Or change each to decimal form and compare places.
Complementary fractionsField Book Lesson 71
- Complementary fractions add to 1.
- Whatever part of the whole one fraction does not claim, its complement does.
Decimal to percentField Book Lesson 72
- Move the decimal point two places to the right.
- A whole number takes two zeros: 2 becomes 200%.
Worked: divide it out
- 78: divide 7 by 8, adding zeros.
- 78 = 0.875
Worked: the complement
- 512 of the cars are loaded.
- The complement of 512 is 712: the unloaded share.
Terms on the record
| Term | Meaning |
|---|
| repeating decimal | a decimal whose digit or block repeats without end, marked with a bar |
| complementary fractions | two fractions that add to exactly 1 |