Introduction
Have you seen how the news channels report the maximum
and minimum temperatures of a particular place on a particular day.
thirty four point three degree Celsius twenty-one point two degree Celsius.
When you go for your regular checkup
Does your doctor check your body temperature and report it as ninety eight point four degrees Fahrenheit?
the dots you see in these figures are known as decimals and these figures are known as
decimal numbers
In This lesson let us look at decimal numbers in great detail
Objectives
At the end of this lesson you'll be able to:
Understand decimal.
Relate fraction and decimal.
Represent decimal on number line.
Compared to decimals.
Let us understand the concept of decimal using fractions with denominator 10.
Consider the fraction bars
In The first bar only 1 out of the 10 blocks has checks.
In the second bar only 2 out of the 10 blocks have waves.
Similarly in the third bar 5 out of the 10 blocks have stripes.
In all these cases we expressed the share of the patent blocks to the total blocks as a fraction with
denominator 10.
Such fractions are called tenths
Thus while one part is 1/10
two parts show two tenths and five parts represent five tenths
One tenth can be written as zero point one in decimal notation
to tenth as zero point two and
5/10 as
zero point five.
Let us now learn to read and write decimals.
consider the example
14 plus 2 plus 1/10, you know that 40 plus 2 is 42
Adding one tenth to it will make it forty two point one
consider another example
30 plus three plus two tenths will be thirty three point two.
Fifty plus nine plus five tenths will be fifty nine point five.
Let us read these numbers from the table
2 tenths and 2 ones and
One 1/10 make forty two point one
Three tenths and three ones and two tenths make thirty three point two
similarly five and nine ones and five tenths make
59.5
Now we will learn to represent decimals on number line.
We will learn this through an example of representing zero point six on number line.
first draw a number line
Mark, the zero and one points on it.
Divide the length between zero and one into ten equal parts.
Each part is called 1/10
we know that zero point six is more than zero and less than one.
and There are six one tenths in it. So count six parts from zero and market
Similarly we can represent two point seven by counting two ones and seven 1/10.
If we know that a fraction with denominator ten can be represented using decimals.
Now let us learn to convert fractions with denominator 2 of 5 into decimals
Take the example of 12 upon 5
First convert the denominator of the fraction into 10 in order to know how many tenths are involved
To know the number of tenths multiply and divide the given fraction by 2
This gives the new fraction
24 upon 10. So we have two ones and four tenths or two ones and
0.4. Which makes it 2.4?
consider another example
Convert 3 upon 2 into a decimal
the denominator of the fraction is 2
To know the number of tenths involved multiply and divide the fraction by 5
Thus the new fraction is 15 upon 10
So we have 1 + 5 1/10 which make it
1.5
Another way to convert such fractions is to simply divide the numerator by the denominator
One part in hundred equal parts is called 100
Small square is called one hundredth of the whole square
In decimal notation we read it as 0.01
Twelve shaded square will make 12 hundredths or 0.1
233 shaded squares will make thirty three hundredths or 0.33
Fifty-two shaded squares will make 52 hundredths or 0.5 to
Now concentrate on the table and let us read decimals from it
Look at the first row
Forty plus five tenths plus three hundredths will make forty point five three
Now focus on the second row
Four hundreds plus 3 tens plus two ones plus six tenths and eight
Hundredths will make four hundred thirty two point six eight
Now pay attention to the third row
Seven hundredths plus eight tenths plus five hundredths will make
seven hundred eighty point zero five
We can extend the place value table further from hundreds to thousands.
latest test our understanding
by solving some questions
right eight hundred plus 60 plus nine plus
3 tenths plus eight hundredths plus four thousandths as a decimal.
800 plus 60 plus 9 is
869.
three tenths plus eight
Hundredths plus four thousandths is point three plus point zero eight plus
.004 which adds up to .384
So the answer is eight hundred sixty nine point three eight four
Let us solve one more question
Write 473 and for hundreds as a decimal in this number
473 is the whole part.
The decimal part is 4 hundredths, which can be written as point. Zero four
So the number is four hundred seventy three point zero four.
Decimals with the same number of decimal places are called like decimals and decimals.
With different number of decimal places are called unlike decimals.
In order to compare decimals,
Convert unlike decimals into like decimals.
This can be accomplished by an xing trailing zeros to the number that has a shorter decimal part
An xing zeros in the end will not make any difference to the value of the decimal
compared
0.05 with zero point 1
We can write 0.1 as zero point one zero
Because there are two decimal places in
0.05
Now it is easy to tell that zero point one zero is greater as it represents 10 hundredths
whereas zero point zero 5 represents
five hundredths
Compare the three numbers
five hundred forty two point five five hundred forty two point five six and
five hundred forty two point five six one.
All three numbers have same whole number part, but their decimal parts are different
Convert all unlike decimals into like decimals by adding zeros at the end
The numbers now will be five hundred forty two point five zero zero
Five hundred forty two point five six zero and five hundred forty two point five six one
Now concentrate on the decimal part alone
the first number represents
five hundred thousands
second number represents
Five hundred sixty thousand and the third number represents five hundred sixty one thousand
so five hundred forty two point five six one is greater than five hundred forty two point five and
five hundred forty two point five six
Similarly five hundred forty two point five six is greater than five hundred forty two point five
Thus five hundred forty two point five six one is greater than five hundred forty two point five six
Which is greater than five hundred forty two point 5.
Summary
Let us summarize what we have learnt:
if We divide a block into ten equal parts each part
represents 1/10.
1/10 can be written as 0.1 in decimal notation.
Every fraction with denominator 10 can be written in decimal notation.
if We divide a block into hundred equal parts each part represents 100,
100 can be written as
0.01 in decimal notation.
Every fraction with denominator hundred can be written in decimal notation
All decimals can be represented on a number line
Every decimal can be written as a fraction and vice versa
Any two decimals can be compared among themselves
