Question
A football ground seats 28 750 people when it is full.
(a) Write 28 750 correct to the nearest thousand.
(b) One day 17 250 people attended a football match.
Work out 17 250 as a percentage of 28 750.
▶️Answer/Explanation
(a) To write 28,750 correct to the nearest thousand, we look at the hundreds digit, which is 7. Since 7 is greater than or equal to 5, we round up the thousands digit.
28,750 rounded to the nearest thousand is 29,000.
(b) To calculate 17,250 as a percentage of 28,750, we divide 17,250 by 28,750 and then multiply by 100.
(17,250 ÷ 28,750) × 100 = 0.6 × 100 = 60
Therefore, 17,250 is 60% of 28,750.
Question
Kyle scores 84 marks out of 96 in an examination.
Work out his percentage mark.
▶️Answer/Explanation
To calculate Kyle’s percentage mark, we divide his score by the total possible marks and multiply by 100.
Percentage mark = (Kyle’s score / Total possible marks) × 100
Percentage mark \(=\frac{84}{96}\times 100\)
Percentage mark \(= 0.875\times 100\)
Percentage mark = 87.5%
Therefore, Kyle’s percentage mark in the examination is 87.5%.
Question
Calculate 17.5% of 44kg.
▶️Answer/Explanation
To calculate 17.5% of 44 kg, we multiply 44 kg by 17.5% expressed as a decimal.
17.5% can be written as 0.175 in decimal form.
17.5% of 44 kg = 0.175 × 44 kg
= 7.7 kg
Therefore, 17.5% of 44 kg is 7.7 kg.
Question
Work out 72 cents as a percentage of 83 cents.
▶️Answer/Explanation
To calculate 72 cents as a percentage of 83 cents, we divide 72 cents by 83 cents and then multiply by 100 to convert it to a percentage.
\(\frac{72}{83}\times 100% = 0.867\times 100% = 86.7%\)
Therefore, 72 cents is 86.7% of 83 cents.
Question
(a) A mass of 300 kg is increased by 8%.
Work out the increase in mass.
(b) Nelson scores 27 out of 40 in a history test.
Work out his score as a percentage.
▶️Answer/Explanation
(a) To calculate the increase in mass, we can multiply the original mass by the percentage increase.
Increase in mass \(= 300 kg\times 8% = 300 kg \times 0.08 = 24 kg\)
Therefore, the increase in mass is 24 kg.
(b) To calculate Nelson’s score as a percentage, we divide the actual score by the total possible score and multiply by 100.
Percentage score \(=\frac{27}{40}\times 100%= 0.675 × 100% = 67.5%\)
Therefore, Nelson’s score is 67.5% in the history test.