THE COMPOUND // FIELD NOTES // WEEK 28
Repeating decimals, the Discard method, and number values
Field Book
Lessons 104 to 107
Due
Test 25 due ยท Supplement 28
Method
Paper first, every step
Escape 7 posts this week. Lesson 105 brings the Discard method for stubborn trinomials: list the candidates, discard the liars.
What you have to be able to do
- Convert repeating decimals to fractions and place numbers in their subsets
- Factor trinomials whose lead coefficient is not one
- Handle three by three systems where each equation carries two variables
The procedures
Decimals to fractionsField Book Lesson 104
- Terminating decimals read straight off place value.
- For repeating blocks, put the block over as many nines, then reduce. Every such number is rational: place it in its subsets.
The Discard methodField Book Lesson 105
- List the factor pairs of a and of c, then write the candidate binomials.
- Test middles and discard until one candidate gives bx exactly.
Three equations, two variables eachField Book Lesson 106
- When every equation has two variables, chain them: solve one, feed the next.
- Substitution runs the whole chain without a five column layout.
Numbers and numeralsField Book Lesson 107
- A numeral is the written symbol. The number is the idea it names.
- Value word problems: digits carry place value, so 10T + U names a two digit number.
Worked: a repeating block
- Convert 0.181818... to a fraction.
- The block 18 goes over 99: 1899.
- Reduce: 211.
Terms on the record
| Term | Meaning |
|---|
| repeating decimal | a decimal whose block of digits repeats forever |
| subset | a set wholly contained in another set |
| numeral | the written symbol that names a number |