Decimals
Decimal numbers are
just another way of expressing fractions. Every fraction can be written
as a decimal, and every decimal can be written as a fraction.
Sometimes it is
necessary to convert decimals to fractions because the fractional form of the
number may be easier to work with than the decimal form. For instance, it is easier to find the
square root of 1/4 than 0.25. However, if the answer choices are in decimal form, work with
the decimal form in your computations.
In a decimal number,
such as 0.357, the first digit to the right of the decimal point, which is 3 in
this example, is the tenths digit (i.e. 1/10), the 5 is the 100ths digit (1/100), the 7 is the 1000ths
digit (1/1000), etc. To convert a decimal to a fraction, use the decimal number (without the
decimal point) as the numerator, and put it over the appropriate denominator (How?). For
example, 0.357 = 357/1000. Then reduce if possible.
To convert a fraction
into its decimal equivalent, divide the numerator by the denominator. For
example,
3/4 = 3 
4 = 4
= 0.75
28
20
20
0
When adding and subtracting decimals,
you must realize that all numbers can be written with
a decimal point. For example, 12 can be written as 12.0. You must know where the decimal
point should go in order to add and subtract decimal numbers. To add and subtract decimals,
line up the decimal points in a column and add the digits as you would in any addition problem.
If decimal points are missing, put them in at least mentally. You may even want to put zeros in
the columns to the right of the decimal point to make the columns line up evenly. For example,
34.5 34.500
87 87.000
123.456 123.456
+ 0.98 + 0.980
245.936 245.936
When multiplying
decimals, first multiply the numbers as you would integers. Next, count the
total number of digits to the right of the decimal points in the two numbers you are multiplying.
Finally, count that number of digits from right to left in your product and put the decimal point
there. For example:
3.4517
x 80.9
279.24253
Since 3.4517 has four decimal places
and 80.9 has one, the product has five decimal places.
When dividing
decimals, convert the divisor into a whole number by moving the decimal point
to the right. Hence, you must move the decimal point in the dividend the same number of places
to the right. After performing the division, the decimal point in the quotient goes directly above
the decimal point in the dividend. In the division problem 24
1.25, 1.25 is the divisor and 24 is
the dividend. Before dividing, change the problem to 2400
125:
24/1.25= 2400/125 = 125
= 19.2
125
1150
1125
250
250
0
To determine
which of two decimal numbers, such as 0.00099 and 0.001, is larger or
smaller, (1) vertically align the decimal points, and (2) fill in the missing zeros. For example,
0.00099 = 0.0009
0.001 = 0.00100
Now it is obvious
that 100 is larger than 99, so 0.001 is larger than 0.00099.
It is often helpful
on the GRE to remember that money is based on the decimal system. For
example, $.98 is 98/100 of a dollar. Hence, $5.98 means 5 dollars plus 98/100 of a dollar. If
you are stuck on a decimal problem, reminding yourself of this fact may help you.
1. readin'
