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UNIT 2. DECIMAL NUMBERS AND SEXAGESIMAL SYSTEM
1. DEFINITION OF DECIMAL NUMBER
"Decimal Number" usually means there is a Decimal Point.
The digits to the left of the point are in the ones, tens, hundreds, thousands (and so on infinitively)
place. Digits to the right of the decimal point are tenths, hundredths, thousandths (and so on ) place.
17.591 = 1 tens is 10, 7 units is 7, 5 tenths is 0.5, 9 hundredths is 0’09 and 1 thousandths is 0’001
2. READING A DECIMAL NUMBER
You can read a decimal number in two ways:
Read the number after the decimal pointas a whole number and give itthe name of its last
decimal place.
Examples:
0’234 is read as two hundred thirty-four thousandths
3’12 is read as three (units) and twelve hundredths
Another way to read a decimal is:
Examples:
0’234 is point, two-three-four
3’12 is three, point, one-two 23’4 Ξ twenty three, point, four
3. CONVERTING FRACTIONS TO DECIMALS.
We can convert fractions to decimals dividing the numerator by the denominator.There are three
different types of decimal number:
An exact or terminating decimal is one which does not go on forever, so you can write down
all its digits. For example: 0.125
Recurring decimal is a decimal number which does go on forever, but where some of the digits
are repeated over and over again. For example: 0.1252525252525252525... is a recurring
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decimal, where '25' is repeated forever. Sometimes recurring decimals are written with a bar
over the digits which are repeated, or with dots over the first and last digits that are repeated.
Other decimals are those which go on forever and don't have digits which repeat. For example
pi = 3.141592653589793238462643...
4. OPERATIONS WITH DECIMALS:
a) ADDING OR SUBTRACTING DECIMALS
To add or subtractdecimals,followthesesteps:
Write down the numbers, one under the other, with the decimal points lined up
Put in zeros so the numbers have the same length
Then add or subtractnormally,remembering to put the decimal point in the answer
b) MULTIPLYING DECIMALS
Just follow these steps:
Multiply normally, ignoring the decimal points.
Then put the decimal point in the answer: it will have as many decimal places as the two
original numbers combined. (just count up how many numbers are after the decimal point in
both numbers)
Example: Multiply 0.03 by 1.
3 × 11 = 33
0.03 has 2 decimal places, and 1.1 has 1 decimal place, so the answer has 3 decimal places:
0.033
Explanation:Because when you multiply without the decimal point (which makes it easy), you are really
shifting the decimal point to the right to get it out of the way.Then we do the (now easy) multiplication:
3. × 11. = 33. But remember, we did 3 Moves of the decimal point, so we need to undo that:
c) DIVIDING A DECIMAL NUMBER:
BY A WHOLE NUMBER: To dividea decimal number by a whole number uselong division,and
justremember to lineup the decimal points.
BY A DECIMAL NUMBER: The trick is to convert the number you are dividingby to a whole
number first,by shiftingthe decimal pointof both numbers to the right:
Now you are dividingby a whole number, and can continue as normal.
