Ray's New Higher Arithmetic · Arts. 162–163 · Unit 9: Decimal Fractions
42. Multiplying decimals
Goal: Your student multiplies decimals and places the point, and knows the idea of a shortened product kept to a set number of places.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Multiplication of decimals (definition, the example 2.56 × .184, rule, remarks, examples) and Oughtred's method for keeping only a set number of decimal places (example 3.8640372 × 1.2479603 to seven places), with examples. Answers are printed.
The lesson, step by step
Warm-up
Mental: .5 × 6; .3 × .3; 2.5 × 4.
The idea
Read:
Multiplication of Decimals is finding the product when either or when each of the factors is a decimal.
Point off as many decimal places in the product as there are decimal places in the two factors.
Work the book's example
2.56 × .184: as whole numbers 256 × 184 = 47104. Two places plus three places is five: .47104. The book shows why: 256/100 × 184/1000 = 47104/100000.
Guided practice
Together:
64.01 X .32
.0001 X 1.006
(20.4832; .0001006, where ciphers are prefixed to fill the places.)
Contracted multiplication
Read Oughtred's method:
may be used when the product of two decimals is required for a definite number of decimal places less than is found in both factors.
Walk through the book's worked example slowly. It is mostly of historical interest now; one example is enough.
Independent practice
Your student works a selection of the ordinary examples.
Check
Answers are printed.
Wrap-up
Ask: Why is .3 × .3 = .09 and not .9? (Tenths of tenths are hundredths.)
Tip
Contracted multiplication was a time-saver before calculators. Treat it as optional enrichment.