Ray's New Higher Arithmetic · Arts. 147–156 · Unit 9: Decimal Fractions

39. Decimal fractions: notation

Goal: Your student explains what a decimal is, names the decimal places to billionths, and reads and writes decimals.

⏱ About 40 minutes · 7 steps

Open it at the Internet Archive ↗

You'll need

  • The book
  • A slate, small whiteboard or scrap paper
  • A notebook and pencil

What's in the book

Decimal fraction defined, decimal places, the decimal point, pure, mixed and complex decimals, three principles about moving the point and annexing ciphers, the table of decimal orders, rules for reading and writing decimals, examples to read, and seven examples to write (no answers printed).

The lesson, step by step

  1. Warm-up

    Ask: How do you write 3 dimes as part of a dollar? ($.30.) 7 cents? ($.07.)

  2. The idea

    Read:

    A Decimal Fraction is a fraction whose denominator is 10, or some product of 10

    The orders of integers decrease from left to right in a tenfold ratio

    The places at the right of units are called decimal places

  3. Kinds and principles

    Read:

    A pure decimal consists of decimal places only

    A mixed decimal consists of a whole number and a decimal written together

    Decimal ciphers may be annexed to, or omitted from, the right of any number without altering its value.

    Show: .5 = .50 = .500. Moving the point one place right multiplies by 10: .032 becomes .32.

  4. Reading

    Read the rule:

    Read the number expressed in the decimal places as the numerator

    then give it the name of the last place. Work the book's example: .0325 is three hundred and twenty-five ten-thousandths. Your student reads the examples on the page.

  5. Writing

    Read:

    Write the numerator as a whole number; then place the decimal point so that the right-hand figure

    stands in the place named. The book's example: eighty-three thousand and one billionths = .000083001.

  6. Independent practice

    Your student writes the seven Examples to be Written, beginning:

    Five tenths.

    Twenty-two hundredths.

    Answers are below; the book prints none.

  7. Wrap-up

    Ask: Is .5 bigger than .45? (Yes: .50 against .45.)

Answers to the book's problems

Examples to be written: 1) .5 2) .22 3) .104 4) 2.01 5) .1605 6) .00087 7) .0000029½

Worked out for this site from the scan. If a number in your copy differs, trust the book.

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