Rounding numbers is a strange phrase, isn't it? The Arabic numerals
like 0, 2, 3 and 9 already have a rounded shape so does rounding numbers
mean changing the shape of 1, 4 and 7? No, we've just having some
fun and joking a bit! Rounding numbers applies to decimal numbers
and not to integers.
A decimal number is composed of an integer for the whole number to
the left of the decimal point and the fractional part to the right
of the decimal point. Rounding numbers means shortening the number
of digits to the right of the decimal point to make the number easier
to work with. The numbers to the right of the decimal point usually
show small amounts and sometimes it's okay to ignore very small amounts.
When you round a decimal number, sometimes you change the last number
that you show. If the decimal digit that you are truncating (removing)
is 5 or more then you add 1 to the last digit that you keep. This
is called rounding up. It sounds complicated but it isn't. Here are
12.3742 rounds to 12.37 because 4 is less than
18.4593 rounds up to 18.46 because 9 is greater
Let's review how to convert fractions to decimal. You probably remember
that 1/2 in fractions is the same as 0.5 in decimal. The 5 in 0.5 is
the same as half of 10 or 10 divided by 2.
What happens when you try to represent 1/3 in decimal? This time
you are trying to divide 10 by 3. The answer in fractions is 3 1/3.
But, wait a minute, 1/3 is what we trying to show in decimal in the
first place. The fraction 1/3 becomes 0.3333333333 with as many three's
at the end as you wish to show. There just isn't an exact match between
the fraction 1/3 and how it's written in decimal.
Use 1. Handling the mismatch between fractions and decimal
One use of rounding numbers is shorten all the three's to the right
of the decimal point in converting 1/3 to decimal. Most of the time,
you will use the rounded numbers 0.33 or 0.333 when you need to work
with 1/3 in decimal. In fact, you usually work with just two or three
digits to the right of the decimal point when there is no exact equivalent
to the fraction in decimal. How would you show 1/6 in decimal? Remember
to round up!
Use 2. Changing multiplied results
What is the answer if you multiply 25 by 75? You get 1875. Now multiply
0.25 by 0.75. You get 0.1875. You started with 2 digits to the right
of the decimal point and ended up with 4. Many times you will just
round up the result to 0.19.
Use 3. Taxes
When you shop, do you pay a state sales tax? If the sales tax is
3% and you by something for $56.30 how much sales tax do you pay?
$56.30 x 0.03 = $1.689 Tax is $1.69
Use 4. Do calculations in your head
Let's pretend that you and your friends are going to a fast food
restaurant and you want to be sure to have enough money to pay the
bill. You can round the cost of each meal to the nearest dollar and
add the amounts quickly and easily.
Use 5. Getting an estimate
Sometimes you want to round integers instead of decimal numbers.
Usually you are interested in rounding to the nearest multiple of
10, 100, 1,000 or million. For example, in 2006 the census department
determined that the population of New York City was 8,214,426. That
number is hard to remember and if we say the population of New York
City is 8 million it is a good estimate because it doesn't make any
real difference what the exact number is.