Decimal Fractions

A fraction in the denary system of powers of ten is called a decimal fraction. It was shown earlier (page 3) that dividing a power of ten by ten decreases the index by one so that <m:mrow> <m:msup> <m:mrow> <m:mn>10</m:mn> </m:mrow> <m:mn>2</m:mn> </m:msup> <m:mo>&#x00F7;</m:mo><m:mn>10</m:mn><m:mo>=</m:mo><m:msup> <m:mrow> <m:mn>10</m:mn> </m:mrow> <m:mn>1</m:mn> </m:msup> <m:msup> <m:mrow> <m:mn>10</m:mn> </m:mrow> <m:mn>1</m:mn> </m:msup> <m:mo>&#x00F7;</m:mo><m:mn>10</m:mn><m:mo>=</m:mo><m:msup> <m:mrow> <m:mn>10</m:mn> </m:mrow> <m:mn>0</m:mn> </m:msup> </m:mrow> </m:math>]]</EquationSource><EquationSource Format="TEX"><![CDATA[$${10^2} \div 10 = {10^1},\;{10^1} \div 10 = {10^0}$$ . This can be extended to negative powers, so that <m:math display=&#x2019;block&#x2019;> <m:mrow> <m:msup> <m:mrow> <m:mn>10</m:mn> </m:mrow> <m:mn>0</m:mn> </m:msup> <m:mo>&#x00F7;</m:mo><m:mn>10</m:mn><m:mo>=</m:mo><m:msup> <m:mrow> <m:mn>10</m:mn> </m:mrow> <m:mrow> <m:mo>&#x2212;</m:mo><m:mn>1</m:mn> </m:mrow> </m:msup> </m:mrow> </m:math>]]</EquationSource><EquationSource Format="TEX"><![CDATA[$${10^0} \div 10 = {10^{ - 1}}$$ .