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Question

Dear Mitch,

I am home-schooling my daughter and was doing fine with the math until we came to why .2 x .2 does not equal .4.

I tried different methods that I found in books and on the internet, but she still doesn't 'get it'. (Though she does answer it correctly because she at least gets that I am correct.) But what should I tell her about why .2 x.2 = .04, and NOT .4?

Yours truly,

Jessica's Mom

Teaching From Home, Pennsylvania

Answer

Dear Jessica's Mom,

Try this:

Go over 'place values'. In other words, the names of the different positions before and after the decimal point.

So, when you get to the decimal point, reading from left to right you have:

decimal point, then tenths, then hundredths, then thousandths, etc.,

like this:

. t     h     t

  e     u     h

  n      n    o

  t       d    u

  h       r    s

  s      e    a

          d    n

           t    d

           h     t

           s     h

                  s


So, .2 x .2 =

two-TENTHS times two-TENTHS =

2/10 x 2/10 =

4/100

-- since when we multiply a fraction by a fraction the procedure is to multiply "across", i.e., we multiply the 'top' (numerator) by the 'top' (numerator) and the 'bottom' (denominator) by the 'bottom' (denominator).

And using the place value labels we reviewed above, we write 4/100 like this:

.04

(So that the 4 is in the "hundredths" place.)

 

Hope that helps,

Mitch