MULTIPLY BY POWERS OF 10
DIVIDE BY POWERS OF 10

PROBLEMS

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11.  True or false?

11.  a)  628 × 10 = 6,280  True.        b)  6.28 × 10 = 6.280  False.      

11.  c)  6.28 × 10 = 62.8  True.

12.  Complete the following with either "left" or "right".

12.  a)  To multiply a decimal by 10, move the decimal point one place
12.  a)  right.

6.75 × 10 =  67.5

12.  b)  To divide a decimal by 10, move the decimal point one place
12.  b)  left.

6.75 ÷ 10 = .675

13.  Multiply each number by 10.  Then multiply by 100; by 1000. 
13.  Move the decimal point.

  5.62 39.5 .006 .0035
× 10 56.2 395 0.06 0.035
× 100 562 3,950 0.6 0.35
× 1000  5,620 39,500 6 3.5

14.  Calculate by moving the decimal point or by adding on 0's.

a)  3.46 × 10,000 = 34,600   b)  28 × 10,000 = 280,000
 
c)  0.009 × 100,000 = 900   d)  0.006 × 1,000,000 = 6,000
 
e)  2.5 × 10,000 = 25,000   f)  0.00002 × 100,000 = 2

15.  If one item cost $2.45, then

15.  a)  10 will cost $24.50.

15.  b)  100 will cost $245.

15.  c)  1000 will cost $2,450.

16.  a)  If 2 pounds of cheese cost $11.50, then how much will 20 pounds
16.  a)  cost?  10 times more:  $115.

16. b)  If 4 pounds of coffee cost $21.95, how much will 40 pounds
16. b)  cost?  $219.50

17.  a)  $12.50 = 10 × $1.25

17.  b)  $125 = 100 × $1.25

17.  c)  $1,250 = 1000 × $1.25

18.  Divide each number by 10.  Then divide by 100;  by 1000.
17.  Move the decimal point..

  12.5 6.45  .5 .02
÷ 10 1.25 .645 .05 .002
÷ 100 .125 .0645 .005 .0002
÷ 1000  .0125 .00645 .0005 .00002

19.  Calculate by moving the decimal point.

a)  68.4 × 10 = 684   b)  68.4 ÷ 10 = 6.84
 
c)  68.4 × 100 = 6,840   d)  68.4 ÷ 1000 = .0684
 
e)  .005 × 1,000,000 = 5,000   f)  .05 ÷ 10,000 = .000005

10.  How many decimal places has each number?

10.  a)  423.6  One.          b)  4.236  Three.          c)  4,236  None.

10.  d)  .05  Two.             e)  6.2000  Four.

11.  Calculate each column.  Separate the correct number of decimal11.  places.

 435 ÷ 10 = 43.5   92 ÷ 10 = 9.2   8 ÷ 10 = .8     
 435 ÷ 100 = 4.35   92 ÷ 100 = .92   8 ÷ 100 = .08
 435 ÷ 1000 = .435   92 ÷ 1000 = .092   8 ÷ 1000 = .008
435 ÷ 10,000 = .0435   920 ÷ 10 = 92   8000 ÷ 100 = 80

12.  Divide by 10.  Then divide by 100.

$340   $25   $8.00
$34   $2.50   $.80
$3.40   $.25   $.08

13.  Complete the following with the correct operation -- multiplication 13.  or division by a power of 10.

a)  1800 = 18 × 100   b)  3 = .003 × 1000
 
c)  .025 = 25 ÷ 1000   d)  .6 = 6 ÷ 10

14.  Scientific notation.  Each of these is written in scientific notation. 14.  What normal number is it?

a)   2.401 × 103  =  2,401   b)   1.006 × 10²  =  100.6
 
c)   7.01 × 105  =  701,000   d)   3.248 × 10  =  32.48  
 
e)   1.86 × 10−4  =  0.000186   f)   4.05 × 10−1  =  0.405
 
g)   6.0 × 10−6  =  0.000006   h)   3.1 × 10−2  =  0.031

15.  Write each of the following in scientific notation.

a)   1,234  =  1.234 × 103   b)   12.34  =  1.234 × 10
 
c)   123.4  =  1.234 × 102   d)   2,400,000  =  2.4 × 106
 
e)   0.000081  =  8.1 × 10−5   f)   0.00395   =  3.95 × 10−3
 
g)   0.00000000628  =  6.28 × 10−9   h)   0.107   =  1.07 × 10−1

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