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CHANGING DECIMALS TO FRACTIONS
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The concepts for this exercise are summarized below.
For a complete discussion, read the text.
Consider again the place values in the base ten number
system.
If we move from left to right, notice that the place value is successively divided
by ten:
-
100010
=100 ;
the thousands place is followed by the hundreds place
-
10010
=10 ;
the hundreds place is followed by the tens place
-
1010
=1 ;
the tens place is followed by the ones place
This pattern continues, after first putting a decimal point to the right of the ones place:
- one divided by ten is one-tenth; the first place to the right of the decimal point is the
tenths place;
- one-tenth divided by ten is one-hundredth; the second place to the right of the decimal point is the
hundredths place; and so on.
Be certain to notice the difference between hundred and hundredth.
Hundred
is to the left of the decimal point, and hundredth is to the right of the decimal point.
The place values are "mirrored" about the ones place, adding "th" to the
right of the decimal point:
The first place to the right of the decimal point has place value
1
101
=110
.
The second place to the right of the decimal point has place value
1
102
=1100
.
In general, the nth place to the right of the decimal point has place value
1
10n
.
A base ten number that uses a decimal point is called a decimal.
Thus, 2.5 and
0.0003 are called decimals, but 3 is not called a decimal.
If there are no digits to the left
of the decimal point, then it is good practice to put a zero in the ones place: that is,
write 0.02 , not .02 .
To read decimals aloud, start by using the prior rules
for reading the part to the left of the decimal point.
Read the decimal point as and.
Only the right-most place value is used for reading the part to the right of the decimal point,
as illustrated in the following examples:
- read 2.03 as two and three hundredths
- read 23.457 as twenty-three and four hundred fifty-seven thousandths
- read 0.000042 as forty-two millionths
Notice that the word and should ONLY be used for the decimal point.
Resist the temptation to insert the word and anywhere else!
Reading a decimal like 972.28936 following the rules above gets a bit tedious.
Thus, it is often read as nine hundred seventy-two point two, eight, nine, three, six.
That is, say point to represent the decimal point, and then just read each digit, separately,
that follows the decimal point.
The number 0.237 can be viewed as
2⋅1
10+3⋅
1100
+7⋅1
1000
or can alternately be viewed as
237⋅1
1000=
2371000 .
Recall that in a fraction ND
, the top is called the numerator and
the bottom is called the denominator.
For example, in the fraction
23100
, the numerator is 23 and the denominator is 100 .
To go from a a decimal to a fraction, you use the right-most place value to determine the correct denominator;
the entire number (without the decimal point) becomes the numerator.
In particular, the number of zeros in the denominator is the same as the
number of places to the right of the decimal point.
Here are some examples:
0.0013=13
10000
(four places to the right of the decimal point; four zeros in the denominator)
23.107=23107
1000
(three places to the right of the decimal point; three zeros in the denominator)
0.72=72
100
(two places to the right of the decimal point; two zeros in the denominator)
If you're rusty on fractions, don't worry—they will be reviewed in a future section.
In this web exercise, you will practice renaming decimals as fractions.
Don't simplify any fractions: leave 0.4 as 4/10, instead of reducing it to 2/5.
Use a forward slash ( / ) to indicate a fraction:
for example, 0.032 gets renamed as 32/1000 .
Do NOT insert commas in any numbers: type in 32/1000 , NOT 32/1,000 .
Use the last reported place value for your new name, even if it is zero:
for example, report 0.50 as 50/100 , NOT 5/10 .