DECIMALS

Decimal Numbers
Decimals were known by the early Chinese
during the Tang dynasty 618 - 906 AD.
During this time they created a positional
decimal numerical system. In the west the
Dutch mathematician Simon Stevin (1548-1620)
is usually credited with advancing the
concept of decimals.

Place Value
Decimals, like whole numbers are based on
a place value system of notation. ex. In
the whole number 123, the 1 has a grater
value than the 3 because of its location.
If it were 123 dollars, the 1 would be
worth 97 dollars more than the 3, just
due its location.
Decimals continue this system of place
value. For ex 34.567. The digits to the
right of the decimal point are less than
one. The closer the digit is to the
decimal point the greater its value.
For example if we refer to money again
\$27.39. We find that the 3 has a greater
value than the 9. The 3 has a value of
\$.30 and the 9 represents \$.09. Does the
3 have a  greater value than the 2 in
this example? The value of each place or
location from left to right starting
with the first place to the right of the
decimal point are in order called tenths,
hundredths, thousandths, ten thousandths,
hundred thousandths, millionth, ten
millionth, ....
Try these examples:
1) 98.54367 write down what place
each number is located in.
(click for answer)
(Check the answer for each
example before you go on to the
next example. If you get the
wrong answer STOP and try to
understand  where you may your
mistake. Then do that problem
over.)

2) 345.67278 write down what place

each number is located in.
Check your answer (click for answer)

Rules for rounding off decimals:

Ex.  34.5672  Round off to the hundredths place.
The 6 is in the hundredths  place. Look at the
digit to the right (which is 7) Is it 5 or more?
Yes.  So we add 1 to the 6  and the number

34.5672 is rounded off to  34.5700. It is customary to

drop the zeros,  so the answer is 34.57

RULES
1. Locate the place you want to round off  to.
2. Look at the first digit to the right of the place you
are rounding off to.
3. If this digit to the right is 5 or more add 1 to the
digit in the rounded  off place and change all of
the digits to the right to zero.
4. If the digit to the  right  is less than 5, change
all of these digits  to the right to zero and don't
alter the digit in the place being rounded off too.
Let us  clarify this with an example.

Ex.  45.67389  Round off to the hundredths place.
7 is the digit in the hundredths place and 3 is
the first number to the right. Since 3 is less than
5,   45.67389 rounds off to 45.67000 or the
preferred 45.67

PRACTICE

1.  round off to the hundredths place 378.9764  click for answer
2.  round off to the tenths place     5.739    click for answer
3.  round off to the thousandths place  45.9995   click for answer