Download Decimal Numbers 1000 100 ones 1 10 01 = . 1 100

______________
Decimal Numbers
1000
100
ones
Thousands Hundreds Units
Whole number side on the left
1
1
1
1
= 01
.
= .01
= .001
= .0001
10
100
1000
10000
. Tenth Hundredth Thousandth Ten Thousandth
Fraction side on right of decimal point
The fraction side becomes smaller when move further to the right
Decimal Numbers consist of a whole part, decimal point and fraction part
For example 0.23, 12.345, and 0.675 are examples of decimal numbers
Decimal numbers increase on left side and decrease on the right side of the decimal point
Reading and Writing Decimal Numbers
• The number of digits after the decimal point will determine the number of decimal
places in the number.
• The last digit in the number will determine the label used to write decimal
numbers in words
To write decimal number in words, write the number in words like regular whole numbers then attach the label.
EXAMPLE#1 Write 0.4 in words
SOLUTION: 0.4 has one digit to the left of the decimal point. Therefore the label is tenth
0.4 read as four tenth
EXAMPLE#2 Write 0.35 in words
SOLUTION: 0.35 has two digits after the decimal point so the label is hundredth.
0.35 is read as thirty five hundredth
EXAMPLE#3 Write the number 0.247 in words
SOLUTION: 0.247 has three decimal places, therefore the label is thousandth
0.247 read as two hundred forty seven thousandth
EXAMPLE#4 Write 0.0027 in words
SOLUTION: 0.0027 has four decimal places after the decimal point: therefore the label is ten thousandth
0.0027 is twenty seven ten- thousandth
EXAMPLE#5 Write 123.36 in words
SOLUTION: 123.36 have two decimal places. The word ‘and’ is used to represent the decimal point.
123.36 read as one hundred twenty three and thirty six hundredth.
Page#2
Practice Exercises#1
Write the following in words
(1) 0.7
(2) 0.67
(3) 0.569
(4) 0.0006
(5) 567.69
Write Decimals Numbers as Fractions
(1) Decimal numbers less than 1
•
•
•
Decimal numbers less than1 has zero on the whole number side
Decimal number less than 1 is a proper fraction( denominator larger than the numerator)
The number of decimal places will determine the number of zeros in the denominator
EXAMPLE#6 Express 0.7 as a fraction
SOLUTION: 0.7 has one decimal place so this means tenth or one zero in the denominator
7
0.7 =
is a proper fraction
10
EXAMPLE#7 Express 0.35
SOLUTION: 0.35 is two decimal places which means hundredth two zeros
35
7
0.35 =
is reduced as
proper fraction
100
20
EXAMPLE#8 Express 0.237 as a fraction
SOLUTION: 0.237 is a three decimal place number this means thousandth. Three zeros in the denominator.
237
0.237 =
1000
EXAMPLE#9 Express 0.000024 as a fraction
SOLUTION: 0.000024 has six decimal places therefore six zeros at the bottom of the fraction
24
3
reduced as
0.000024 =
1000000
125000
Practice Exercises#2
Express the following as a fraction
(a) 0.06
(b) 0.25
(c) 0.234
(d) 0.00245
Page#3
Note: Decimal numbers ending with zero. If zero is the last digit in the number, the zero can be dropped
Example 0.230 is the same as 0.23.
When the zeros are in front of or between nonzero digits, it cannot be dropped from the number.
Example 0.02 the 0 is in the tenth place and cannot be dropped. This number has two decimal places.
Example 12.304 the 0 is in second place and it cannot be dropped
(2) Decimals Greater Than One
•
•
Decimal numbers greater than 1 are mixed fractions which can be
express as a improper fractions
Convert the decimal part to a fraction using the number of decimal
places to determine the number of zeros
EXAMPLE#10 Express 2.3 as a fraction
SOLUTION: 2.3 one decimal place on the right of the decimal point.
3
2.3 = 2
which is a mixed fraction
10
EXAMPLE#11 Express 1.04 as a fraction
SOLUTION: 1.04 is two decimal places = 1
4
1
this reduced as 1
100
25
EXAMPLE#12 Express 26.0271
SOLUTION: In the number 26.0271, 1 is in the ten thousandth place and 26.0271 is a four decimal place
number which means four zeros in the denominator
271
26.0271 = 26
10000
Practice Exercises#3
Change the following decimals to a fraction If possible, reduce the fraction
(a) 5.24
(b) 4.08
(c) 2.1875
(d) 3.7
(e) 5.0003
(f) 135.124
Page#4
Exercises
1. In the number 0.23457
a. How many decimal places in the number
b. What digit is in the tenth place
c. What digit is in the thousandth place
d. What digit is in the ten-thousandth place
2. Write the decimal numbers in words
a. 0.34
b. 0.045
c. 7.08 d. 567.56
e. 68.0567
f. 0.000275
g. 2.5
h. 19.34
3.
(a)
(b)
(c)
(d)
Write the decimal numbers
Nine hundredth
Two and three thousandth
Seven hundred twenty thousandth
Two hundred thirteen and twenty five ten-thousandth
4.
(a)
(b)
(c)
(d)
(e)
(f)
Change the decimal numbers to a fraction reduce the fraction to the lowest term
0.66
0.08
7.003
34.75
0.302
13.00025
Answers
Page#5
Changing Fractions to Decimals
a
The fraction
can be express as terminating or a non-terminating decimal number.
b
In order to change fractions to a decimal divide the numerator by the denominator.
a
=b a
b
4
to a decimal number
5
0.8
4
= 0.8 terminating decimal
SOLUTION: 4 divided by 5 = 5 4.0 , therefore
5
7
EXAMPLE#14 Change
to a decimal
8
0.875
7
SOLUTION: 8 7.000 therefore = 0.875 terminating decimal
8
1
EXAMPLE#15 Change mixed fraction 3 to a decimal
4
SOLUTION: Ignore the whole number and change the fraction part to decimal number then add it to the whole
number part.
0.25
1
1
1
1
Since 3 = 3 +
and
= 4 100
. , 3 + 0.25 = 3.25 therefore 3 = 3.25 terminating decimal
4
4
4
4
EXAMPLE#13 Change
3
to a decimal
8
0.375
3
3
SOLUTION: 2 + = 2 + 8 3.000 = 2 + 0.375 = 2.375 Therefore 2 = 2.375
8
8
EXAMPLE#16 Change 2