68 Part 1: The World of Numbers
Decimal Fractions
By now you’re familiar with the fractions that are called common, the ones written as a quotient.
Now it’s time for a look at decimal fractions. They’re fractions that only use denominators that
will fit into the decimal, or base ten, system. Decimal fractions have denominators of 10, or
100, or 1000 and so on, but you hear the denominator in the name rather than seeing it under a
fraction bar. The common fraction 103 has a numerator of three and a denominator of 10, so you
read it as “three tenths.” When that same number is written as a decimal fraction, it’s 0.3. It’s still
read “three tenths,” because the 3 is in the tenths place.
The places that follow the decimal point of a number are assigned to be tenths, hundredths,
thousandths, and so on, so that the place value tells the denominator. 0.1 is 1 tenth, and 0.01 is 1
hundredth. What would have been the numerator of the fraction becomes the digit in the place
that corresponds to its denominator. 0.7 is 7 tenths, the equivalent of 107 , 0.008 is 8 thousands,
or 10008 , and 0.91 is 91 hundredths, or 10091. When you write a fraction in the decimal system, the
denominator seems to disappear, but you hear it if you give the decimal its proper name.MATH TRAP
While many people will say “point–3-7-5” for 0.375, its real name is “three hundred
seventy-five thousandths.” The “three hundred seventy-five” is the numerator and the
“thousandths” names the denominator.Place a dot, called a decimal point, to the right of the ones digit of a number. This is the divider
between the whole and the parts. You’ve probably seen this idea used to write dollars and cents.
Three dollars and 12 cents might be written $3.12. This says 3 whole dollars (left side of the
decimal point) and 12 pennies, part of a dollar (right side of the decimal point).Numbers Less than One
Our decimal system is able to represent cents as part of a dollar, but
also to represent even smaller parts of any whole, again by working
with tens. Decimal fractions, as their name says, are still based on
tens. On the left side of the decimal point, as you move to the left,
away from the decimal point, the value of that place gets bigger.
Specifically, it gets ten times larger. On the right side of the deci-
mal point, each time you move to the right away from the decimal
point, the place value will get smaller. With each step, you’ll break
the piece into ten smaller pieces.(^4675) ones. tenthshundredthsthousandths