Faster than light

Faster than light

Pencil and paper
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This task is about converting between ordinary numbers to standard form.
 
illustration: spaceship
 
The speed of light is about 3 × 108 m/s (metres per second). The starship Venus can travel at warp speeds that are faster than the speed of light. Warp speed is the number of times faster than the speed of light Venus is travelling. At warp speed 2, Venus is travelling at two times the speed of light. This is 6 × 108 m/s in standard form.
 
a)   Write the warp speed for the following
 
 
i)
 
ii)
 
iii)
9 × 108 m/s. Warp speed __________
 
1.8 × 109 m/s. Warp speed __________
 
3 × 109 m/s. Warp speed __________
 
 
b)   Write each of these speeds in standard form.
 
 
i)
 
ii)
 
iii)
Warp speed 8. ____________________ m/s
 
Warp speed 40. ____________________ m/s
 
Warp speed 100. ____________________ m/s
Task administration: 
This task is completed with pencil and paper only.
Copyright: 
Image: PxFuel
Level:
5
Curriculum info: 
Maths, Number and Algebra, Number Knowledge
Key Competencies: 
Using language, symbols, and texts
Keywords: 
standard form, multiplication, division
Description of task: 
Students perform calculations on numbers in standard form and convert numbers from standard form to ordinary form and vice versa.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Multiplicative thinking, sets 8-9
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  

Y10 (11/1999)
a) i)
ii)
iii)		 3
6
10		 moderate
very difficult
very difficult
b) i)
ii)
iii)		 2.4 × 109
1.2 × 1010
3 × 1010		 very difficult
very difficult
very difficult
Diagnostic and formative information: 
   Common error Likely reason
a) i)
    ii)
    iii)		 900 000 000
1 800 000 000
3 000 000 000		 Writes number in ordinary form.
a) iii) 1 Increase in the power of 10 between 3 × 108 and 3 × 109.
b) i)
    ii)
    iii)		 24 × 108
120 × 108
300 × 108		 Writes correct answer but not in standard form.
b) i)
    ii)
    iii)		 8 × 108
40 × 108
100 × 108		 Interprets warp number as the power of 10.