Please have some flexibility!

READING DECIMAL NUMBERS

Imagine playing a game with the following three decimal number cards:

0.4 = Four tenths

0.45 = Forty-five hundredths

0.375 = Three hundred seventy-five thousandths

You might be asked to put these in order from least to greatest. You might be asked to add these all up to find a final sum. You might be asked to shade in a 10 X 10 grid in a way that represents the amounts shown. In fact, students will be asked to all of the above.


A few simple things will always makes matters work out better:

First, since out students are so tuned in to comparing fractional amounts through conversion to equivalent percents, why not convert decimals to percents? But how?

Well, it's easy enough for most kids to see that 0.4 (four tenths) could be written as 4/10, and most know that we could multiply 4/10 X 10/10 to get 40/100. Once we have a denominator of 100, we have a percent (parts per hundred). So, 0.4 = 40%.

For 0.45 (forty-five hundredths) we just think 45/100, and we have our percent. 45%

Now for the challenging one, not really, if we look at .375 (three hundred seventy-five thousandths) we could write 375/1000. If we divide 375/1000 by 10/10 we get 37.5 /100 or 37 1/2 percent. so, if you were shading in a 10 by 10 grid, you would simply shade thirty-seven and one half blocks.

If I was asked to add these decimals, I would rewrite them so that they all have the same number of digits on the right hand side of the decimal point. 0.4 = 0.40 = 0.400 = 0.4000000000000000000000000000000000000000000.

0.45 = 0.450 etc.

I'd end up with:

0.400
0.450
+0.375

From there, I would add the largest place value (the tenths) .4 +.4 +.3 = 11/10 or 1.1
Next, I would add the hundredths .00+.05 +.07 = 12/100 or .12
Finally, I would add the thousandths .000 + .000 +.005 = 5/1000 or .005

1.1
.12
+ .005 = 1.225 or 1 22/1000 or 1 22.5/100 or 122 1/2 %



Have Fun :-}