Working with standard form II

Working with standard form II

Pencil and paper
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This task is about calculating numbers in standard form.
Fill in the boxes for each of these calculations below in standard form.
 

E.g., The number 3.1 × 102 is written in the boxes as:  × 10 kilometres.
 
a)		  
Light travels approximately 3 × 105 kilometres in one second.
How far does light travel in ...
 
  i)  3 seconds?  × 10   kilometres

Optional working space
 
 		  
  ii)  7 seconds?  × 10  kilometres
 
 		  
  iii)  1000 seconds?  × 10  kilometres
 
 		  
  iv)  3.2 × 107 seconds?  × 10  kilometres
       (approx. 1 year)

b) A space ship travels 4.5 × 103 kilometres in one hour.
How far will it travel in ...
 
  i)  100 hours?  × 10  kilometres

Optional working space
 
 		  
  ii)  2.4 × 101 hours?  × 10  kilometres
       (i.e., 1 day)
 
 		  
  iii)  1.67 × 10-2 hours?  × 10  kilometres
       (approx. 1 minute)
Task administration: 
This task is completed with pencil and paper only.
Level:
5
Curriculum info: 
Maths, Number and Algebra, Number Knowledge, Number Strategies
Keywords: 
standard form, multiplication
Description of task: 
Students perform calculations using standard form.
Answers/responses: 
  

Y10 (09/1999)
a) i)
ii)
iii)
iv)		 9, 5
2.1, 6
3, 8
9.6, 12		 moderate
very difficult
difficult
difficult
b) i)
ii)
iii)		 4.5, 5
1.08, 5 NOTE: Accept 1.1 or 1.10.
7.515, 1 NOTE: Accept 7.47 to 7.52 instead of 7.515.		 difficult
very difficult
very difficult
Diagnostic and formative information: 
    Common error Likely calculation Likely reason
a) ii)
    iii)
    iv)
b) i)
    ii)
    iii)		 21, 5
3000, 5
96 000 000, 5
45, 4; 450, 3
10.8, 4; 108, 3
75.15, 0 ;.07515, 3		    Correct answer, but not in standard form.
a) i)-
b) iii)		       Correct decimal part, but incorrect power of 10.
a) i)
    ii)
    iii)
b) i)
    ii)		 9, 15
21, 35
3000, 5000
450, 300
108, 72		 3 × 3 = 9; 3 × 5 = 15
7 × 3 = 21; 7 × 5 = 35
1000 × 3 = 3000; 1000 × 5 = 5000
100 × 4.5 = 450; 100 × 3 = 300
24 × 4.5 = 108; 24 × 3 = 72		 Multiplies exponents rather than adding them (and answers not in standard form).