DECMIAL NUMBERS
A
Decimal Number (based on the
number 10) contains
a Decimal Point.
<<The word "Decimal" really
means "based on 10">>
Example
In the number 17.3,
the point separates 17 from the 3. 3 is in the tenth
position.
=> 3 of tenths = 3 of 1/10 = 3/10
Thus, as a
fraction, it is 3/10
So, 17.3 is 17 and
three tenths or 17 3/10
RELATING TO PLACE VALUE:
Value is the positional value of the digit in the number
When we write
numbers, the position (or ‘place’) of each digit is important.
Example:
·
the "6" is in the Ones position,
meaning 6 ones (which is 5),
·
the "5" is in the Tens position
meaning 5 tens (which is fifty),
·
and the "4" is in the Hundreds position,
meaning 4 hundreds.
As we move left,
each position is 10 times bigger!
Tens are 10 times bigger than Ones
Hundreds are times bigger than tens
Putting in the decimal Point
456.37 has 4 hundreds, 5 tens, 6
ones and 3 tenths and 7
hundredth
=> 400 +50 + 6 + 3/10 + 7/100
Example:
What is the value
of the digit 6 in each of the following?
a. 64.2
Step: Write Place-Value
above the number
H T O. T H
6 4. 2
The value of digit
6 is 60
b. 34.6
Step: Write
Place-Value above the number
H T O. T H
3 4. 6
The digit 6 is 0.6
DECIMAL: From WORDS TO NUMBERS
Decimal number in
words has ‘~th’,
‘tenth’ is the first decimal place,
‘hundredth’ is the second decimal
place and
‘thousandth’ is the third decimal
place (seen from the place value table)
REMEMBER:
Words with ‘th’ is for decimal place.
METHOD
Example: Convert thirty tenth to number form
Step1: UNDERLINE whole number and double
underline ‘th’ words.
thirty
tenth
Step2: WRITE: 0 . t, h, th
Step3: PUT number with last digit at tenths
H T 0 . t, h, th
0 . 3 ( place a 0 at the one position if no
whole number)
Example
Convert twenty and thirty-three
thousandths to words
Step1: UNDERLINE
whole number and double underline ‘th’ words.
five hundred and twenty and thirty-three
thousandths
Step2: WRITE:
T O . t, h, th
Step3a: Write the whole number
H T 0 . t, h, th
5 2 0
Step3b: PUT decimal number with last digit at
thousandth
H T 0 . t, h, th
5 2 0.
0 3
3
WORD TO NUMBERS (Whole number and decimal)
If there are whole
numbers and decimal, ‘breaks’ the words and ‘add’ back.
Example:
Write 4 hundred, 5 tenths and 6
thousandths in number form.
Step1: Underline whole number and double underline
‘th’ words.
4 hundred, 5 tenths and 6 thousandths
Step2: Write: 0 . t, h, th
Step3: Arrange numbers below “: 0 . t, h, th” and
Add the numbers
(use Whole Number method for 4
hundred)
0 . t, h,th
400 .
0 . 5
+ 0 .
0 0 6
400 . 5 0
6
ROUNDING OFF
Rounding a number is
to replace it with another number value that is approximately equal but
‘cleaner’ and simpler.
RULE for rounding off (Quick Refresh)
If number is from 0
and to 4, then DROP or Fall
(4) off / let it go
If number is from
5 to 9, then ADD 1 or high
5 --> go higher
ROUNDING OFF FOR DECIMAL
Rounding off for
decimal is similar to whole numbers except that we need to maintain the decimal
places as given in the question.
METHOD
Step 1: Underline the round-off decimal place
required.
Step 2: Circle the number to the right
Step 3: Compare
a. number is 5 or
greater, round-UP, ADD 1 to
underline number
or
b. Less than 5,
round DOWN, DROP, leave
underline number un-change
Step 4: Change numbers to right of underline to 0
Step 5: Adjust number format
a. to nearest whole number: drop decimal place
b. to give decimal places as required
Example1:
Round off to the
nearest whole number, 5.27
Step 1: <Underline whole number> 5.27
Step 2: <Circle number to right> 5.②7
Step 3: <Compare with 5 > 2 is less than 5, DROP: round-down
Step 4: <Change> 5.00,
Step
5: <Adjust number format>
Answer: 5 (no decimal place)
Example2:
Round off to the
nearest 1 decimal place, 4.36
Step 1: <Underline 1st decimal >
4.36
Step 2: <Circle number to right > 4.3⑥
Step 3: <Compare to 5 > – 6 is more than 5,
ADD 1: round-up
-> 3 to 4
Step 4: <Change> number to the right of
underline to 0 ->4.40
Step 5: <Adjust number format> Answer: 4.4 (1
decimal place)
Answer = 4.4
Practice:
1: Round off to
the nearest 2 decimal places, 3.295
2: Round off to
the nearest 2 decimal places, 3.965
1: 3.30 [Must write 0 in 3.30 to show nearest
2 decimals]
2: 4.00[Must write 00 in 4.00 to show nearest
2 decimals]
More Practices
(1) Set 2 numbers
for rounding off to the nearest whole number and 1 decimal.
(2) Tutor to
request students to set 2 numbers for rounding off to the nearest 1 decimal and
2 decimals.
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