Ray's New Higher Arithmetic · Art. 48 · Unit 2: Numeration and Notation
5. Reading and writing large numbers
Goal: Your student reads any number by periods (the French method) and writes numbers given in words, filling empty places with ciphers.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
The list of periods up to vigintillions, the rule for numeration, examples to read, the rule for notation with a worked example, and 21 numbers to write in figures. No answers are printed for these.
The lesson, step by step
Warm-up
Read aloud: 3,040,506. Then 70,000,007.
The rule for reading
Read:
Begin at the right, and point the number into periods of three figures each.
Commence at the left, and read in succession each period with its name.
Look at the book's list of period names. Millions, billions, trillions and quadrillions are the ones used in real life.
The rule for writing
Read:
Begin at the left, and write each period in its proper place
and fill empty places with ciphers. The book's note says:
Every period, except the highest, must have three figures
Work the book's example together: four million twenty thousand three hundred and seven is 4,020,307.
Read the book's examples
Your student reads aloud the numbers under Examples in Numeration, pointing off periods first. Some are very long; that is fine.
Guided practice
Write these two together:
Two hundred and seven thousand four hundred and one.
One million four hundred and twenty-one thousand six hundred and eighty-five.
(207401 and 1421685.)
Independent practice
Your student writes the Examples in Notation, 1 to 21, in the notebook. Check with the answers below; numbers 17, 19, 20 and 21 are long, so check them by reading them back aloud.
Wrap-up
Ask: Why can't you just write "seven million and seventy" as 770? (The empty periods need ciphers: 7,000,070.)
Answers to the book's problems
Examples in Notation: 1) 75 2) 134 3) 204 4) 370 5) 1234 6) 9007 7) 40563 8) 90009 9) 207401 10) 640040 11) 700007 12) 1421685 13) 7000070 14) 10100010 15) 60705000 16) 807040031 18) 19020500000000000. For 17 and 19 to 21, have your student read the written number back by periods to check it.
Worked out for this site from the scan. If a number in your copy differs, trust the book.