** 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**

**
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**
** **