Multiplying Decimals by
0,100,1000,10000
\0(
[000 , [0 000 0M
>I
[OQ i
Quick: R e v i e w
Use mental math to multiply a decimal by 10,100,100ft and 10 000.
/ 2 . 4 5 X 10=* 2 4 5
> Wherfrydu multiply a decimal by 10,
/
0,432X10=* 4.32
the dlgijl shift 1 place to the left
You show this by moving the decimal
\ 6.8 X 10 = 68
point 1 place to the right.
/ 1 . 3 6 7 X 1 0 0 = 136.7
> When you multiply a decimal by 100,
(
5.3 X 100 = 530
the digits shift 2 places to the left
You show this By moving the decimal
\ 0.25 X 1 0 a = * 2 5
point 2 places to the right
> When you multiply a decimal b£ 100ft
/ 5.846 X 1000 = 5846
/ 3.21 X 1000
3210
the digits shift 3 places to theleftf
\ 0.004 X 1000 = 4
Yotl show this by moving the decimal
point 3 places to the right
> When you multiply a decimal by 10 000 / 0.245 X 10 000 = 2450
the digits shift 4 places to the left
( 1.26 X 1 0 0 0 0 = 12600
You show this by moving the decimal
\ 0.8 X 10 000 = 8000
point 4 places to the right
f
: Try These j
la) ic^<4kr
10 = *J3 M
c) 0.461 X 10 =
100 = l^H
0.461 X 100 = ^JoJ
1000 =
0.461 X 1000 = 4 ^ /
Use mental math to find each product
1. a) 6.5 X 10 =
6.5 X 100 =
Qtf
b) 734 X
(Q^O
734 X
6.5 X 1000 = C^OO
734 X
Ik?
6.5 X 10000 = <cbO0D 734 X 10000 = 7 - ^
2. a) 1.9 X 10 =
d) 2.6 X 100 =
g) 2.63
48
X 10 =
°\
Mo
/
b) 6.73 X 100 =
e) 7.2 X 1000 =
h) 1.123
X 100 =
&73
g
0.461 X 10000 = 4 ^ / o
JHj£o
^/2>£>
c) 9.365 X 10 000 =
1X00 f) 0.486
lti>^ i) 0.586
X 1000 =
X 10 000 =
$££o
•V
•4
Practice
Use mental math.
fa)
Jp^eM^
1. Use the information in the table to find the mass
Masses of Coins
of each set of coins.
l
a) 10 000 quarters f^OOO^b)
c) 1000 dimes /
e) 100 toonies
g) 10 nickels
2.
100 nickels
7^D(^
39i
d) 10 pennies 23 « S J
If 3 O a
f)
3 9< 5^ Q
e? .,
1000 nickels ? ? 5 b <j
h) 10 000 dimes / 7^0 0
Coin
Mass (g)
Penny
2.35
Nickel
3.95
Dime
1.75
Quarter
4.4
Toonie
7.3
Multiply.
a)
5.03
X 10
6.714
X 100
b)
c)
d)
0.415
X 1000
62.3
X 10 000
6> i3
e)
62.345
X 1000
f)
8.173
X 10 000
0.542
X 100
g)
no
m
S
»
OOD
3.7
X 1000
h)
2.
31 DO
3. Write each distance in metres.
a) 6.59 km fp b90/M
d) 3.8 km i
&^C7
M
c)
b) 0.927 km
e
) 5.47 km
m
C^0_m
37.459 km
f) 6.28 km £
? 7 V
3
*n
4 . One bottle of spicy sauce has a capacity of 0.725 L. What is the capacity of
10 bottles?
1'2^L
1000 bottles?
L 10000 bottles?
7^S^oL
5. The width of a quarter is 23.88 m m . What is the distance covered by each
number of quarters laid side by side?
a) 10
£3 9. 9
M/M
b)
ioo 3 3 6 9 m^i
c) IOOOO
23 d %QD
^ S t r e t c h Your Thinking
1. Use the table in Practice question 1 to find the mass of:
a) 101 pennies
c) 11 quarters
7*?^
?8.7y
^
b) 1001 nickels
^d) 110dimes
19so
3?S"3.qs^
I 9-?-^
49
f- ^ 5
Mu Itiplying Who[e I P %
]
Numbers by O.T 0.01,0.001
r
0*1/ 0*01
0.001 ate <C
}
QU2GI(
Review
Use mental math to multiply a whole number by 0.1,0.01, and 0.001 T
> When you multiply by OA, the digits shift 1 place to thgrighfc,
To show this, move the decimal point 1 place to theleft.
/f\UlfStp
27 X 0.1 = 2.7
>• When you multiply by 0.01, the digits shift 2 places to the right.
To show this, move the decimal point 2 places to the left.
27 X 0.01 = 0.27
>
a
O
When you multiply by CL001, the digits shift 3 placesto the right.
To show this, move the decimal point 3 placesjojhejeft.
27 X 0.001 = 0.027
TffTfiese )
Use mental math to multiply;
0*7
1. a) 2 X 0.1 =*
b) 74 X 0,1 = _
235X0.1 =
2 X 0.01 = 0-0 7
74 X 0.01 =
235 X 0.01
2 X 0.001 = P, ODl
74 X 0.001 = •0.07Y
235 X 0.00T =
0<f
d) 5 X 0.1 =
5 X 0.01 = O'O^
60 X 0.01 =
5 X 0.001 = CP. OPf
2. a) 13 X 0.1 =
6.0
e) 60 X 0.1 = .
b) 52 X 0.001
O-g'f
e) 3 X 0.01 =
0.06
= 0. Oi'Z
ML
g) 519 X 0.001 = O&Cf h) 152 X 0.1 =/ f . J
d) 59 X 0.01 =
j ) 7 X 0.1 =
sa
0, 7
k) 6 X 0.001 =
f) 1 6 4 X 0 . 1 =
164X0.01
60 X 0.001-
^ J
0,2^-
164 X 0.001
c l 8 X 0.01 = . o.og
f) 231 X 0.001
= Q.13J
i) 6 X 0.001 =
73 X 0.01 =
Q-73
Practice
Use mental math to multiply.
1. a) 20 X 0.01 = 0,10
d) 7 X 0.001 =
M13
b) 63 X 0.001 =
0*007
0-0h
e) 3 X 0.01 =
c) 9 X 0.1 -
0.°f
f ) 568 X 0.01 =
g) 354 X 0.1 = 33^7 h) 28 X 0.1 - Q* 8
£±£3
i) 158 X 0.001 =
QJfB
2. Complete the table.
Number
39
H7
ira
je
x 0.1
x 0.01
3 • 9"
0,039
4.7
0.H7
1S r J
1.52
0.098
0*19*1
194
a)
75
X 0.1
b)
1
X 0.001
9
X 0.01
c)
o.ool
7*f
e)
x 0.001
d)
13
X 0.1
h)
486
X 0.1
0.7V
154
X 0.01
f)
71
X 0.01
g)
62
X 0.001
0 tO 6 2~*
4. One jellybean has a mass of 0.001 kg. What is the mass of 98 jellybeans?
O-Do/x
9B -
/r f / t mass o£ ?&
0<Q?g
*J^6e&t.
Stretch Your Thinking
A flower seed has a mass of 0.1 g.
What is the mass of 200 of these seeds?
-
O* /x
How many seeds would it take to make 0.5 kg?
( kct ~ /bOO
30*$J
iTQ.QO f •t^dj
-
17
#fctXT,
f
53
UNIT
4
' .. . ,
Drvidfntt Decimals by
10,100,1000,10000
Quick
Review
Use mental math to divide a decimal by 10,100,1000, and TO OOO.
3 . 6 2 * 10=0.362
When you divide a decimal by 10, t
8 . 7 * 10 = 0.87
the digits shift 1 place to the right
You show this by moving the decimal
6.8 * TO = 0.68
point % place to the teft;
When you divide a decimal by 100,
1 . 6 3 * 100=0.0163
the digits shift 2 places to the right.
5 . 6 * 100 = 0.056
You show this by moving the decimal
3 * 100 = 0.03
point 2 places to the left.
When you divide a decimal by 1000,
4.415 * 1000 = 0.004 15
the digits shift 3 places to the right
7.2 * 1000=0.0072
You show this by moving the decimal
1 * 1000 = 0.001
point 3 places to the left.
When you divide a decimal by 10 000,
7 . 5 * 10000=0.00075
the digits shift 4 places to the right.
1.4* 10000=0.00014
You show this by moving the decimal
6 * 10 000 = 0.0006
point 4 places to the left.
r
it.
rryTfiesa
Use mental math to find each quotient
1. a) 8.2 * 10 =
b) 5 * 1 0 =
0*0
8.2 * 1 0 0 =
8.2 * 1000 =
8.2 * 10000 =
2.
a)
3.4 * 10 =
d\
05*100=
g) 5.17 * 10 =
SO
L
5 * 100=
O.OObl
5 * 1000=
O-OOPBl
O'lH
5 * 10000 =
b) 1 . 6 3 * 100 = &#f£3
0. 00fe)
0*£fl
0»*>'
8 * 10000 =
h) 9.6 *
^ ^ 1
0*0Of
0, OOOf
c) 1.12 * 1000 = 0*60
f j 7 * 10000 =
1000^0_ D0lh 0
£
0*0^
6382 * 10 =
f/3
0-00O7
0*1,1% 2
Practice
Use mental math.
1. a) 0.23 - M O = 0*0 ^3
c) 78.3
1 0 0 0 = 0,0
b) 6 * 10 000 = Q. 0OO(>
76 3
d) $ 8 . 9 0 * 10 =
e) 0.47 * 1000 = 0. OOP H 7
^o.8y
f) 2.146 * 100 =
0.0X7#£
2. Write the missing divisor in each division sentence,
a) 4.23 *
c) 5 *
70Q
/OQ
e) 0.12 *
= 0.0423
b) 0.738 *
= 0.05
/OOP
d) 3.2 *
= 0.000 12
f)
(O
= 0.0738
/o OOP
173 + /p
= 0.000 32
OOP
= 0.0173
3. A pile of 10 000 sheets of paper is 85 cm thick.
~ 6S~-r (o ODD
0- OQQfo^i
What is the thickness of 1 sheet of paper?
4. One hundred 50C coins have a mass of 690 g.
What is the mass of one 50C coin?
(eo^Cj.
~& ^0 r lOO
5. Jacob's scarf is 79 cm long.
Write this length in as many different units as you can.
11-.(oo*o-
7? rvt
7f x<0'= 7?c?M/h
lo-- 79
ct*
. ^ n m ^ , , — —
6.
Sandy drank 575 mL of water during her walk.
7<T'-f (000
Write this a m o u n t in litres.
/T)7.
Keshav j o g g e d 1257 m today.
(k*A-
-
Cl^
Q, ^JbT
/&C?0
fa
Write this distance in the units indicated.
JJs<7W000
-f'lS'fkm:
cm;
12 S7o
What is the mass of 1 seed?
'lOO-foOQ-
/ ^ \ Stretch Your Thinking
^ " ~ L ) n e quarter has a mass of 4.4 g.
A bag of quarters has a mass of 2.64 kg.
What is the total value of the quarters? _
(m ~/oO
0*3
~
(
C
cwi
o
°
/W - /
m
a
/
{
J i L ^ m m
^T)8. Helena's hair is 6.4 d m long. Write this length in metres.
9. One thousand seeds have a mass of 200 g.
^
L
I
dm;
J
~ ^OOj^L^
c
& - f -r /D ^
Q.j)H
m