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Topic 4
D E C I M A L S
2 3 .9 12.6
1 . 0 9
0 .6 8
0. 7 78 9
0. 0 0 4 3
R M 3 4.5 0
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Decimalse !se "ecimals
e#e$%"a%. &o$ e'ample()*e p$ices o+ )*i,-s e
/!% a$e $i))e, i, )*e+o$m o+ "ecimals.
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5.67 m
M% *ome
To sc*ool
Sale
RM4.99
59.8 m
39.5C1.5A
1.75 li)e$
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Loo a) )*e p$ices o+ )*e )*i,-s
i, )*e pic)!$es /elo. om!c* )*e p$ices o+ )*e )*i,-s
RM1(820.99 RM19.95 RM30.55
RM30.55
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Ca, %o! $i)e )*e mass o+
#e$-es as a "ecimal !si,- )*e
!,i) ilo-$am -. Ca, %o!
see )*e mass o+ )*is #e$-es
+$om )*e scale /elo
Decimals a$e !se"
*e, e ,ee" )o
-i#e mo$e acc!$a)e$ea"i,-s )*a) *ole
,!m/e$s ca,,o)
-i#e.
3.5kg
1
2
3
4
5
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Decimal is a ,!m/e$ )*a) $ep$ese,)s a
+$ac)io, i, *ic* )*e "e,omi,a)o$ is
i, )*e +o$m o+ 10( 100( 1 000.
0.32 32 100
0.4 4 10
3.89 389 100
0.067 67 1000
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Rep$ese,)i,- &$ac)io,s 1 a," 1 as Decimals
10 100
a," #ise #e$sa.
Decimals a$e ,!m/e$s *ic* $ep$ese,)
+$ac)io,s i)* "e,omi,a)o$s s!c* as 10(
100 o$ 1000.
3 10
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Rea"i,- $i)i,- Decimals
a 0.3 Zero point three.
/ 79.86 Seventy-nine point eight six.
c 4.0012 Four point zero zero one two.
" 387.605 Three hundred eighty-seven pointsix zero five.
e RM34.25 Ringgit !"!ysi! thirty-four !ndtwenty-five #ents.
+ RM0.45 Forty five #ents or Ringgit !"!ysi!zero point four five.
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C*a,-i,- &$ac)io,s I,)o Decimals
a 1 2
1 : 2 0.5 510
/ 8 13
c 11 20
" 3 2 5
e 1 3 8
To c*a,-e +$ac)io,s i,)o "ecimals( "i#i"e
)*e ,!me$a)o$ /% )*e "e,omi,a)o$
8 : 13 0.615 615
1000
11 : 20 0.55 55100
17 : 5 3.4 3410
11 : 8 1.375 1375
1000
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C*a,-i,- Decimals i,)o &$ac)io,
To c*a,-e "ecimal i,)o +$ac)io,( looa) )*e ,!m/e$ o+ "ecimals -i#e,. I+
)*e$e is o,l% o,e "ecimal place( )*e
"e,omi,a)o$ ill *a#e o,l% o,e ;e$o.T*e, $i)e )*e "ecimal as a +$ac)io,
i)* a "e,omi,a)o$ o+ 10( 100 o$ 1000.
Simpli+% )*e +$ac)io, i+ possi/le.
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C*a,-e )*e +olloi,- "ecimals i,)o
+$ac)io,s
a 0.9 0.9 1 "ecimal place )*e$e+o$e( 9 10 1 ;e$o
/ 0.87
c 0.403
" 2.574
e 76.45
+ 0.0038
$" % "
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$"!#e %!"ue1 As i)* *ole ,!m/e$s( a "i-i) i, a "ecimal
*as a place #al!e. T*e )a/le /elo s*os
)*e place #al!es +o$ "ecimals.
, i ) s
D e c i m a l
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=al!e ?+ Di-i)
Eac* "i-i) i, a "ecimal *as i)s o, #al!e.
T*e #al!e o+ a "i-i) is "e)e$mi,e" /% i)splace #al!e. I, "ecimal 789.163( )*e place
#al!e o+ )*e "i-i) 6 is *!,"$e")*s.
T*e$e+o$e( )*e #al!e o+ "i-i) 6 is 6 o$ 0.06 100
S)a)e )*e ,!m/e$ o+ )*e places i, )*e+olloi,-.
a 89.431 / 16.56 c 307.25
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& Compa$i,- a," ?$"e$i,-
Decimals
&A""i)io,( S!/)$ac)io,( M!l)iplica)io,
a," Di#isio, o, Decimals
2 3 .9
@ 12.6
1 . 0 9
@0. 7 78 9
@ 0. 0 0 4 3
R M 3 4.5 0
0 .6 8
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Compa$i,- Decimals
'hi#h of these de#i(!"s h!s ! gre!ter v!"ue)
45.0976 o$ 45.0915* +ow do you #o(p!re
these two de#i(!"s*
45.0976
45.0915
T*!s( 45.0976
is -$ea)e$ )*a,
45.0915
,n order to #o(p!re these two de#i(!"s)
!rr!nge the( !##ording to their p"!#ev!"ue. Then st!rt #o(p!ring fro( the
"eft.
I"e,)i+% )*e la$-e$ ,!m/e$ o+ )*e
+olloi,- pai$sa 0.8 a," 0.188
/ 3.095 a," 3.099
c 56.28 a," 56.286
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A,% "ecimal i)* a
#al!e less )*a,
;e$o is a ,e-a)i#e"ecimal.
@0.25 @[email protected] @0.10 @0.5
00.50 1.00 1.50 2.00 2.50
Be-a)i#e "ecimals posi)i#e "ecimals
;e$o
A,% "ecimal i)*
a #al!e -$ea)e$
)*a, ;e$o is a
posi)i#e "ecimal.
oo" o/
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@10 @6@8 @4 @2 0@20 @18 @16 @14 @12
Loo a) )*e ,!m/e$s o, )*e li,e ,!m/e$ /elo.
! -0 !nd /1
- !nd -2
# 0 !nd -5
d - !nd -3
e -1 !nd -14
@12
@6
0
@3
@14
Compa$e )*e ,!m/e$s -i#e, a," "e)e$mi,e *ic* ,!m/e$ is -$ea)e$.
T*e ,e-a)i#e
si-, maes)*e "ecimal
,!m/e$
smalle$ )*a,)*e -$ea)e$
,!me$ical
#al!e.
i 6 i "
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rr!nging 6e#i(!"s
Decimals ca, /e a$$a,-e" i, o$"e$ !si,- a
,!m/e$ li,e o$ /% compa$i,- )*ei$ #al!es.Re!rr!nge the fo""owing nu(ers in in#re!sing order
7! 0.32( 0.34(0.39( 0.37( 0.31
Me)*o" 1 D$a
a ,!m/e$ li,e
i)* )e, e!al
i,)e$#als. Ma$
o++ eac* i,)e$#al
i, *!,"$e")*s(
+$om 0.30 )o 0.40
0.30 0.320.31 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40
Me)*o" 2
A$$a,-e )*e
,!m/e$s
acco$"i,- )o
)*ei$ place #al!e
0.32
0.34
0.39
0.37
0.31
Compa$e )*e *!,"$e")*s
a," $ea$$a,-e )*e o$"e$
0.31
0.32
0.34
0.37
0.39
0.31( 0.32( 0.34( 0.37( 0.39
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Ro!,"i,- ?++ DecimalsDecimals ca, /e $o!,"e" o++ )o a -i#e,
,!m/e$ o+ "ecimal places.Le)s sa%( e
a,) )o $o!,"
)*e ,!m/e$
3.6489 )o 2"ecimal places.
A ,!m/e$
$i))e, )o 2
"ecimal places
*as )o "i-i)s
a+)e$ )*e "ecimal
poi,).
S)ep 1
I"e,)i+% )*e seco," "ecimal place a,"
ma$ i) i)* a slas*.
3.64 F 89
1s) "ecimal places
2," "ecimal places
3$" "ecimal places
S)ep 2Loo a) )*e ,!m/e$ i, )*e )*i$" "ecimal
place. Si,ce 8 is -$ea)e$ )*a, 5( $o!,"
!p /% a""i,- 1 )o )*e "i-i) 4. T*e$e+o$e(
3.6489 3.65 )o "ecimal places.
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A""i)io, a," S!/)$ac)io, o+ DecimalsTo a"" o$ s!/)$ac) "ecimals( li,e !p )*e "ecimal poi,)s
a," )*e, +ollo )*e $!les +o$ a""i,- a," s!/)$ac)i,-
*ole ,!m/e$s.E'ample &i," )*e s!m o+ )*e +olloi,-.
a 7.45 G 99.2 G 23.79 / 67.305@ 25.29 G 13.84
.45
8.83.
S)ep 1
7.45
G99.20G23.79
130.44
S)ep 2
S)ep 1 Li,e !p )*e
"ecimal poi,)s.
S)ep 2 A"" )*e
,!m/e$s. T*e$e+o$e(
7.45G 99.20 H 23.79 130.44
Ca, %o! +i," )*e a,se$
+o$ !es)io, /
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M!l)iplica)io, ?+ Decimals
&i," )*e p$o"!c) o+
a 3.71 6.4 / 3.56 ' 4.2 ' 6.2
a 3.71
6.4
1484
222623744
2 "ecimal places
1 "ecimal places
3 "ecimal
places
2 "ecimal places G
1 "ecimal place
/ 3.56
4.2
712 1424
14952
' 6.2
29904 89712
927024
2 "ecimal places
1 "ecimal places
1 "ecimal places
2".pG1".pG1".p
3 "ecimal poi,)s
So )*e a,se$ is 23.744So )*e a,se$ is 927.024
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M!l)ipl% 85.34 /% 0.1 a," 0.001
Solution:
85.34 0.1 8. 534 8.534
85.34 0.001 0. 08534 0.08534
M!l)ipl%i,- Decimals
M!l)ipl%i,- "ecimals is !s) lie m!l)ipl%i,-
*ole ,!m/e$s.
o$ 0.001( e mo#e
)*e "ecimal poi,)o,e( )o( o$ )*$ee
places )o )*e le+) )o
+i," )*e a,se$.
e a"" J0K a+)e$ )*e "ecimal poi,)
)o s*o a,o)*e$ place #al!e. I,
)*is case )*e J0K is )*e place
*ol"e$ +o$ )*e #al!e o+ )e,)*s
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6ividing 6e#i(!"s
9y 10)100)1 000) 10 000:
6ivision nswer
a 24.56 : 10
/ 24.56 : 100
c 24.56 : 1000
" 24.56 : 10000
e ca, me,)all% "i#i"e "ecimals /% 10( 100(
1 000( 10 000 /% mo#i,- )*e "ecimal poi,)
o,e( )o o$ )*$ee "ecimal places )o )*e le+).
24.56
24.56
24.56
24.56
2.456
0.2456
0 0.02456
00 0.002456
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6ividing 6e#i(!"s 9y 6e#i(!"s
To divide ! de#i(!" y !nother de#i(!") the divisor shou"d
e #h!nged to ! who"e nu(er.E'ample 42.6 : 1.2 426 : 12
42612
35.5
36
66606060. .
35.5
6ivision nswer
a 0.165 : 0.1
/ 29.376 : 0.01c 5.98 : 0.32
" 93.5 : 2.5
1.65
2937.618.6875
37.4
598 : 32
935 : 25
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Com/i,e" ?pe$a)io,s
1 47.56 12.45 : 2.5
2 2.62 : 1.3 @ 2.3 0.1 G 4.4
3 20.50 : 3.024 : 0.52 G 1.43.59
4 3 G 15 G 6 G 8510 100 1000 10000
Calc!la)e eac* o+ )*e +olloi,-. i#e %o!$
a,se$ co$$ec) )o 3 "ecimal places.
236.849
6.185
18.063
0.465
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Sol#i,-
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Sol#i,-
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Sol#i,-
,ee"% s)!"e,)s i,*e$ sc*ool. I+ eac*
pe, is RM0.43 (
*o "oes s*e *as)o pa% +o$ all )*e
pe,s
Sol!)io,
88 ' 0.43
RM37.84
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Sol#i,-
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Sol#i,-
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