This document discusses decimals, decimal place value, and rounding off numbers. It defines decimals as numbers that have both a whole number part and a fractional part separated by a decimal point. It explains the decimal place value system and how the value of each place decreases by a factor of 10 as you move from left to right after the decimal point. Tenths, hundredths, and thousandths places are defined. Rounding off numbers is described as estimating a number to its nearest value. Rules for rounding whole numbers, decimals, and at different place values like tens, hundreds, thousands are provided along with examples.

1. GROUP 3
DECIMALS, DECIMAL PLACE VALUE
AND ROUNDING OFF NUMBERS

2. DECIMALS

3. What is a Decimal?
 We get decimals when we break a whole into smaller
parts. A decimal number then has two components: a
whole number part and a fractional part. The decimal
place value system for the whole part of a decimal
number is the same as the whole number value system.
However, we get the fractional part of the decimal
number as we move toward the right after the decimal
point. The given image shows the decimal place value
chart:

5.  Note that as we go from left to right in the decimal place value system, each values
is ⅒ times smaller
 The first place after the decimal point is called the “tenths”, which represents a place
value of ⅒ of the whole or one-tenth of the whole. In decimal form, this fraction is
written as “0.1”. than the value to its left.
 Such fractions whose denominator is 10 or a positive power of 10 is called a decimal
fraction.
 The second place is called the “hundredths”, which represents a place value of 1⁄100 of
the whole or one-hundredth of the whole. In numerical form, this decimal fraction is
written as “0.01”.
 And the third place is called the “thousandths”, which represents a place value
of 1/1000 of the whole or one-thousandth of the whole. In numerical form, this decimal
fraction is written as “0.001”.
 Here’s an example of a decimal number 17.48, in which 17 is the whole number, while 48
is the decimal part.

6. DECIMALS
 A decimal is a number that consists of a whole
and a fractional part. Decimal numbers lie
between integers and represent
numerical value for quantities that are whole
plus some part of a whole.

7.  For example, in the given image,
we have one whole pizza and
a half of another pizza. This can
be represented in two ways:
 Fractional form: In fraction form,
we can write that there is one
and one-half of a pizza. That is
1½ pizza.

8.  Decimal Form: In decimal form, we will write this as 1.5
pizzas. Here, the dot represents the decimal point and
the number before the dot, i.e., “1” represents one
whole pizza and the number behind the decimal point
represents the half pizza or the fractional part.

9. DECIMAL PLACE VALUE

10. What is Decimal Place Value?
 Depending upon the
position of a digit in a
number, it has a value called
its place value.
 The value of the digits in the
decimal (base ten) system is
based on the number ten.
 In a place value chart, as we
move from right to left, the
value of each place increases
by 10 times.
 The value of the tens place is
ten times that of the ones
place. The value of the
hundreds place is ten times
that of the tens place and so
on.

11.  When we move from
one place to the next
place on the right
side of a place value
table, the place
becomes one-tenth
⅒ of its previous
place.
 The value of the hundreds place is
⅒ of the thousands place. The
value of tens place is ⅒ of
hundreds place. The value of ones
place is ⅒ of the tens place.

14.  Decimal number may contain a whole number part
and a fractional part (decimal part).
 In case the decimals consist of only one part that is
a decimal part or the whole part, we will write zero
in the whole or decimal part.
Writing Decimal Numbers in the Decimal Place Value Chart

15. Let’s write the following decimals in the place
value table:
 452.123
 1,000.788
 3.409
 33.005
 710.01

16. Understanding the Decimal Place Value Chart
 When looking at the decimal place value chart, you
can see that place values before the decimal point
begin with ones, then tens, hundreds, and so on, but
place values following the decimal point begin with
tenths, then hundredths, then thousandths, and so
on.

18.  The fraction part of the number is represented by the digits following
the decimal point of a decimal number.
 For example, the number 0.46 is made up of 4 tenths and 6
hundredths.
This can also be written as 0.46 = 0.4 + 0.06.
In other words, it means, 0.46 = 4/10 + 6/100.

19. Solved Examples
(a) 14.005
(b) 172.231
(c) 14.3
(d) 423.770
(e) 0.009

20. ROUNDING-OFF NUMBERS

21. What Do You Mean by Rounding Off a Number?
 Rounding off is nothing but estimation.
Estimating the actual number to its nearby
number is called rounding off.

22. Example of Rounding Off from Everyday Life!
When someone asks you the price of
your book, you say 100 even if it is 98.
This is giving an estimation after
rounding off a number. This is how we
apply the concept of rounding off in our
everyday life.

23. How to Round Off Different Numbers?
Whole Numbers
 Different numbers use different ‘rounding off’
rules. Let’s discuss them one by one.
 Whole numbers are rounded off at different place
values.

24. Example:
 If we round off 15,493 to the nearest
tens place then the answer will be
15,490.
 As the unit place is less than 5, the
tens place digit will not change.
 Similarly, if we round off 12,359 to its
nearest tens place then the answer
will be 12,360.
 As the unit place is more than 5, the
tens place digit will change its
successor.
Nearest Ten
 Check the unit place digit:
 If the unit place digit is less
than 5 then keep the tens
place digit the same and put
0 at the unit place.
 If the unit place is 5 or more
than 5 then change the tens
digit into its successor and
put 0 at the unit place.

25. Example:
 If we round off 15,443 to the nearest
hundred places then the answer will
be 15,400. As the tens place is less
than 5, the hundred place digit will
not change.
 Similarly, if we round off 12,359 to its
nearest hundred places then the
answer will be 12,400.
 As the tens place is 5, the hundred
place digit will change to its
successor.
Nearest Hundred
 Check the tens place digit:
 If the tens place is less than 5
then keep the hundred place
digit the same and put 0 at the
tens and unit place.
 If the tens place is 5 or more
than 5 then change the hundred
digit into its successor and put
0 at the tens and unit place.

26. Example:
 If we round off 15,443 to the nearest
thousand place digit then the answer will
be 15,000. As the hundred place digit is
less than 5, the thousand place digit will
not change.
 Similarly, if we round off 12,659 to its
nearest thousand place digit then the
answer will be 13,000.
 As the hundred place digit is more than
5, the thousand place digit will change to
its successor.
Nearest Thousand
 Check the hundred place digit:
 If the hundred place digit is less
than 5 then keep the thousand
place digit the same and put 0
at the hundred, tens, and unit
place.
 If the hundred place digit is 5 or
more than 5 then change the
thousand place digit into its
successor and put 0 at the
hundred, tens, and unit place.

27. Decimal Number
 The concept is quite similar to the whole number with
some minor but noteworthy changes. If the digit right
to the place value you are rounding to is less than 5,
round down. However, if it’s 5 or more than 5, round up.

28. Nearest Whole
 5.9165 rounded to
the nearest whole is 6.
 As 5 is followed by 9
and 9 is greater than 5.
So, round up.
Nearest Tenth
 5.9165 rounded to
the nearest tenth is 5.9
 As 9 is followed by 1 and
1 is smaller than 5. So,
round down.

29. Nearest thousandth
 5.9165 rounded to
the nearest
thousandth is 5.917.
 As 6 is followed by 5. So,
round up.
Nearest Hundredth
 5.9165 rounded to
the nearest hundredth is
5.92.
 As 1 is followed by 6 and
6 is greater than 5. So,
round up.

30. Solved Examples
Example 1.
Round off the following numbers to
the nearest ten:
1) 5,499
2) 3,453
3) 4,405

31. Solution
1) 5,499 rounded to the nearest ten is 5,500.
The unit place digit is more than 5 so add one to the tens place digit.
2) 3,453 rounded to the nearest ten is 3,450.
The unit place digit is less than 5 so the tens place digit will remain the same.
3) 4,405 rounded to the nearest ten is 4,410.
The unit place digit is 5 so add one to the tens place digit.

32. THANK YOU !!!

33. HANDA NA BA KAYO?

34. QUIZ #3
WHAT IS THE DECIMAL
PLACE VALUE OF THE
UNDERLINE ( _ ) NUMBER :
1.) 1,001.1001
2.) 99.99
3.) 6969.69
4.) 886.688
5.) 1111.1111
ROUND-OFF THE FOLLOWING
NUMBERS:
NEAREST THOUSANDS
6.) 6,543.21
7.) 9,499.00
8.) 8,199.75
NEAREST THOUSANDTHS
9.) 0.9999
10.) 1010.1010

35. 1.) 1,001.1001
= THOUSANDTHS
2.) 99.99
= TENS
3.) 6969.69
= HUNDREDTHS
4.) 886.688
= TENTHS
5.) 1111.1111
= THOUSANDS
6.) 6,543.21
= 7,000.00 or 7,000
7.) 9,499.00
= 9,000.00 or 9,000
8.) 8,199.75
= 8,000.00 or 8,000
9.) 0.9999
= 1.000 or 1
10.) 1010.1010
= 1010.101