Answer :
Question 1
Convert the following percentages as fractions:
(i) 276%
Convert to fraction:
[tex]276\% = \frac{276}{100} = \frac{69}{25}[/tex]
(ii) 3 1/7%
Convert the mixed number to an improper fraction, then to a percentage:
[tex]3 \frac{1}{7}\% = \frac{22}{7}\% = \frac{22}{700} = \frac{11}{350}[/tex]
(iii) 0.005%
Convert to fraction:
[tex]0.005\% = \frac{0.005}{100} = \frac{5}{100000} = \frac{1}{20000}[/tex]
Question 2
Convert the following fractions as percentages:
(i) 4/5
Convert to percentage:
[tex]\frac{4}{5} = 0.8 = 80\%[/tex]
(ii) 2 3/5 (as a decimal, 2 3/5 = 2.6)
Convert to percentage:
[tex]2.6 = 260\%[/tex]
(iii) 8/25
Convert to percentage:
[tex]\frac{8}{25} = 0.32 = 32\%[/tex]
Question 3
Convert the following as decimals. Then convert the decimals as percentages:
(i) 7/8
Decimal:
[tex]\frac{7}{8} = 0.875[/tex]
Percentage:
[tex]0.875 = 87.5\%[/tex]
(ii) 5/16
Decimal:
[tex]\frac{5}{16} = 0.3125[/tex]
Percentage:
[tex]0.3125 = 31.25\%[/tex]
(iii) 9/80
Decimal:
[tex]\frac{9}{80} = 0.1125[/tex]
Percentage:
[tex]0.1125 = 11.25\%[/tex]
Question 4
Convert the following ratios as percentages:
(i) 18:25
Convert to percentage:
[tex]\frac{18}{25} = 0.72 = 72\%[/tex]
(ii) 11:18
Convert to percentage:
[tex]\frac{11}{18} \approx 0.6111 = 61.11\%[/tex]
(iii) 21:75
Convert to percentage:
[tex]\frac{21}{75} = 0.28 = 28\%[/tex]
Given the scope of the exercise, these are the detailed solutions for questions 1 to 4. Please let me know if you need solutions for further questions! Notice how each conversion involves a clear understanding of the arithmetic process, ensuring the final representation meets the percentage, fraction, or decimal target as required by the original questions.