Monday, December 2nd, 2019

in math, we continued with decimals.  First, we reviewed place value and did some review exercises that involved finding the value of an underlined number.  For example, take the number 847.45.  The four is underlined and is in the tenths place, so it is 4 tenths.  4 tenths is expressed as 0.4 or 4/10.

Today's lesson involved full expanded notation.  There is a difference between expanded form and full expanded notation.  Expanded form is basically the place value of each digit exposed and added together.  As an example:  123.45 is broken down to 100+20+3+0.4+0.05.  

Full expanded notation shows it in its entirety.  What do I mean by this?  Take the number 97:  it is expressed as 9 x 10.  Why, instead of 90+7?  Because it really delves into what it means.  The nine is in the tens place and there are 9, tens.  So, that can be expressed as 9x10+7.  

Take the number 456.  The four is in hundreds place, so there are four hundreds, or 4x100.  The five is in the tens place, so there is five tens, or 5x10.  The 6 is in the ones place so there are 6 ones, or 6x1.  Since any number multiplied by itself is the same number, it is really unnecessary to write it as 6x1.  The full expanded notation of 456 is (4x100) + (5x10) + 6.  I use the parentheses to group it together and to make it easier to keep track of.  

The key lesson was having decimals.  In this case, we will use the number 34.54 as an example.  There are 3 tens, so it is 3x10.  There are 4 ones, so I write a 4.  The five is in the tenths place, so it is 5 tenths, or 5/10.  The other 4 is in the hundredths place, so it is 4 hundredths or 4/100.  The full expanded notation of 34.54 is:  (3x10) + 4 + (5x1/10) + (4x1/100).