Initial Diagnostic Audit - Unit A6: Number Systems

Do NOT use a calculator for any questions in the audit unless specifically told otherwise
Section A6.1 - Roman Numerals
1. Convert CDLXIV to base 10 Arabic numbers.   
2. Convert 1487 to Roman numerals.   
3. What is LXI - XX? Give your answer in base 10 Arabic numbers.   
4. What is XXVII + LIX? Give your answer in Roman numerals.   
5. What is XIV × CV? Give your answer in Roman numerals.   
Section A6.2 - Number Classification
6. Select all of the numbers below that are irrational numbers.
2
3
√
2
0.55
22
π
7. Select all of the numbers below that are recurring decimals.
1
11
1
10
1
9
1
8
1
7
8.
Write 0.375 as a rational number of the form  
m
   when n ≠ 0 and m and n are integers
n
with no common factors (except 1).

0.375 =   
  
9.
Given that a = 1 + 
√
2
   and b = 1 –  
√
2
 , is

(a) a + b rational or irrational?

(b) ab rational or irrational?

Section A6.3 - Binary Numbers
Convert the binary numbers to base 10.
10. 1111 =
11. 10101010 =
Convert the base 10 numbers to binary numbers.
12. 45 =
13. 1000 =
14. What is the difference between the base 10 number 11111 and the binary number 11111?
Give your answer in base 10.
Section A6.4 - Adding and Subtracting Binary Numbers

Calculate these binary number sums, giving your answers in binary.
15. 1111 + 1010 =
16. 1000 + 1000 + 1000 =
17. 1111 - 1010 =
18. 11000 - 1101 =
19. Below are 3 binary numbers. Add together the two smallest of these numbers.
101101       110000      100111
Give your answer in base 10.

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Produced by Russell Geach for CIMT - January 2013