Working with standard form

Working with standard form

Pencil and paper
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This task is about calculating numbers in standard form.
 
Write your answers for a) to d) in standard form.
  
a)
A satellite travels 4.0 × 104 kilometres when it orbits the Earth once. How many kilometres would the satellite travel after orbiting the Earth 1000 times?
 
Optional space for working
 
 
 
 
Standard form: _____________________ km

 
 
b)
 
The population of Christchurch city is 3.78 × 105 and the population of Wellington city is 2.15 × 105. What is the total population of Christchurch and Wellington cities?
 
Optional space for working
 
 
 
 
Standard form: _____________________ 

 
 
c)
 
New Zealand has 2.89 × 105 beehives and the average hive has 5.0 × 104 bees. What is the total number of bees in New Zealand?
 
Optional space for working 
 
 
 

Standard form: _____________________

 
     
d)
The Sun has a mass of 2.0 × 1030 kilograms and the Earth has a mass of 6.0 ×1023 kilograms. What is the Sun's mass divided by the Earth's mass?
 
Optional space for working 
 
 
 
 
Standard form: _____________________

 
Task administration: 
This task is completed with pencil and paper only.
Level:
5
Curriculum info: 
Maths, Number and Algebra, Number Knowledge
Keywords: 
standard form, addition, multiplication, division
Description of task: 
Students perform calculations in standard form.
Answers/responses: 
   

Y10 (10/1998)
a)  4.0 × 107 moderate 
b)  5.93 × 105 difficult 
c)  1.445 × 1010
NOTE: Accept 1.44 × 1010or 1.45 × 1010.		 difficult 
d)  3.3 × 106 very difficult 
Diagnostic and formative information: 
  Common error Likely reason
a) 
b) 
c) 
d) 		 40 × 106
13.34 × 105or 1334 × 103
14.45 × 109or 1445 × 107
33 × 105or .33 × 107		 Correct answer but incorrect use of standard form. 
b)  13.34 × 1010
13.34 × 103		 Adds numbers but also adds indices. 
Adds numbers but subtracts indices. 
d)  3.3 × 1053
3 × 1052		 Adds rather than subtracts indices.