We already know that
decimals count
smaller and smaller pieces of one — first tenths, then
hundredths. To decide which of two decimals is bigger, we use
the very same place value, working from the biggest pieces down.
First line up the decimal points, then compare the
tenths. The decimal with more tenths is bigger — you can stop
right there. Only if the tenths tie do you move on to the
hundredths.
0.7 > 0.65
Here 0.7 wins because it has seven tenths
while 0.65 has only six — and seven tenths
beats six tenths, no matter what comes after.
Watch out for the most common trap: more digits does not mean
bigger! 0.65 looks longer than
0.7, so it is tempting to call it the larger
number. But length is not value — only place value decides. Compare the tenths
first, and 0.7 clearly comes out ahead.
Press play, then replay it. Two decimals between
0 and 1 are plotted on
the number line; whichever sits further right is the bigger one, and
we say the comparison aloud.