Fundamentals of Mathematics, 2008a

340 CHAPTER 6. DECIMALS
• understand the meaning of a nonterminating division
• be able to recognize a nonterminating number by its notation
Converting a Fraction to a Decimal (Section 6.9)
• be able to convert a fraction to a decimal
Combinations of Operations with Decimals and Fractions (Section 6.10)
• be able to combine operations with decimals
6.2 Reading and Writing Decimals 2
6.2.1 Section Overview
• Digits to the Right of the Ones Position
• Decimal Fractions
• Reading Decimal Fractions
• Writing Decimal Fractions
6.2.2 Digits to the Right of the Ones Position
We began our study of arithmetic (Section 1.2) by noting that our number system is called a positional
number system with base ten. We also noted that each position has a particular value. We observed that
each position has ten times the value of the position to its right.
This means that each position has 1 10
the value of the position to its left.
1
Thus, a digit written to the right of the units position must have a value of
10
of 1. Recalling that the word
"of" translates to multiplication (·), we can see that the value of the rst position to the right of the units
digit is 1 10
of 1, or
1
10 · 1 = 1
10
The value of the second position to the right of the units digit is 1
10 of 1
10 , or
1
10 · 1
10 = 1
10 2 = 1
100
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