{"id":237,"date":"2015-02-18T14:12:13","date_gmt":"2015-02-18T22:12:13","guid":{"rendered":"http:\/\/www.base-ten.com\/tm\/?p=237"},"modified":"2015-02-18T19:08:09","modified_gmt":"2015-02-19T03:08:09","slug":"places-and-bases","status":"publish","type":"post","link":"http:\/\/www.base-ten.com\/tm\/places-and-bases\/","title":{"rendered":"Places and Bases"},"content":{"rendered":"

Recently in math class we have been working with decimals. This is one of the areas in math where a solid foundation in place value will take you a long way. If for instance you want to know the product of 15 and 3.2 it\u2019s nice to know that 10 x 3.2 is simply a decimal move and 5 x 3.2 is just half again. I am always surprised to find that place value is not well understood by 5th<\/sup> grade. I guess I need to stop being surprised. But perhaps place value is just a little more complicated than we give it credit for, and maybe there is just not enough emphasis in the earlier grades.<\/p>\n

Let\u2019s look at the base-ten place value table:<\/p>\n\n\n\n\n\n
Thousands<\/td>\nHundreds<\/td>\nTens<\/td>\nOnes<\/strong><\/td>\nTenths<\/td>\nHundredths<\/td>\n<\/tr>\n
1000<\/td>\n100<\/td>\n10<\/td>\n1<\/strong><\/td>\n1\/10<\/td>\n1\/100<\/td>\n<\/tr>\n
103<\/sup><\/td>\n102<\/sup><\/td>\n101<\/sup><\/td>\n100<\/sup><\/strong><\/td>\n10-1<\/sup><\/td>\n10-2<\/sup><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

The reason for the ease of computations with 10 and powers of 10 is that ten is the base. This is why when you multiply 10 times anything \u201cyou just add a zero.\u201d I try to teach my students to use the more mathematically accurate phrasing of \u201cyou just move the decimal,\u201d but it\u2019s no more challenging. The ones, or units, are the center of the place value system \u2013 all other places are exponentially larger or smaller than the base to the zero power.<\/p>\n

Exponent review:<\/em><\/p>\n