DECIMAL
Decimal
fraction - The
fractions whose denominators are 10, 100, 1000, etc. are called decimal
fractions.
Decimal number
– numbers
written in decimal from are called decimal numbers.
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A
decimal number has two parts, the whole number part and the decimal part.
Decimal places - The number of digits in
the decimal part is the number of decimal places.
e.g.- 4.93 has two decimal places and
7.632 has
three decimal places.
Like decimals -
Decimals
having the same number of decimal places are called like decimals.
e.g.- 9.82, 6.03,14.58
are like decimals, each having two decimal places.
Unlike decimals
- Decimals
having different numbers of decimal places are called unlike decimals.
e.g.- 6.4, 8.93, 12.065
are unlike decimals.
Expanded form - we know that the expanded form of a number
represents that number as the sun of the place-
values of all its
digits.
we can write the expanded form of a
decimal, say 2684.359, in three ways:
ⓐ Expanded form in words:
2684.359
= 2thousand + 6hundreds + 8 tens + 4 ones + 3 tenths + 5 hundredths + 9
thousandths
ⓑ Decimal Expansion:
2684.359
= 2000 + 600 +
80 + 4 + 0.3 + 0.05 + 0.009
ⓒ Fractional
Expansion:
2684.359 =
= 2000 + 600 + 80 + 4 +
Equivalent
Decimals – Decimals
having the same value are called equivalent decimals.
e.g.- 0.3 = 0.30 = 0.300
Therefore, 0.3,
0.30, and 0.300 are equivalent decimals.
Place value
chart
|
Place
|
thousands
|
hundreds
|
tens
|
ones
|
Decimal
point
|
tenths
|
hundredths
|
Thousandths
|
|
Place
value
|
1000
|
100
|
10
|
1
|
.
|
|
|
|
e.g.- the place
value of 6 in 243.56 =
the place value of 4 in 12.498 =
the place value of 0 in 630.007 =
the place value of 9 in 5812.319 =
To
add or subtract decimal numbers write the numbers one below the other so that
the decimal points are in one vertical line. Then add or subtract.
To multiply:
(a) A
decimal number by 10 or powers of 10: Shift the decimal point
to the right by as many paces as there are number of zeros, e.g.,
(b) A
decimal number by a decimal number: Shift the decimal point
and multiply them as whole numbers. The number of decimal places in the product
is the same of the number of decimal places in the multiplicand and multiplier. Thus to multiply 52.8
by 0.917, multiply 528 and 197 and counting from the right, put decimal point
after 4 digits in the product. Thus, 528
To divide:
(a) A
decimal number by 10 or powers of 10: Shift the decimal point to the left by a many places as there number of zeros, e.g.,
(b) A
decimal number by a whole number: Put the decimal point
in the quotient directly above in the decimal point in the dividend. Divide as
with whole numbers.
(c) A
decimal number by a decimal number: Convert the divisor to
a whole number by shifting the decimal point to the right by the same number of
decimal places as there are in the divisor. Then shift the decimal point of the
dividend also by the same number of places to the right. Divide the new
dividend by the whole number divisor. Thus,
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Annexing
zeros to the extreme right of a decimal number does not change its value, i.e.,
0.6 = 0.60 = 0.600 etc.
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If
the numerator and denominator of a fraction contain the same number of decimal
places, then we can remove the decimal point, e.g.,
To change fractions to
decimals, divide the numerator by the denominator.
(a) A fraction
is a
terminating decimal if in its lowest form, the denominator has fractions as
2 or 5 or both 2 and 5, e.g.,
(b) A fraction
is
a non-terminating and repeating or recurring decimal, if a
digit or block of digits are repeated in the decimal part. The block of digits
which is repeated is expressed by putting a bar on the block, e.g.,
,
,
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