ecc4","revisionId":"208ff396-df67-44f1-9fe5-23d1cb017525","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":"medium","totalMarks":2,"sourceTitle":null,"calculatorUse":"non_calc","isCalculation":false,"parts":[{"id":"e7b5210a-a045-4a3a-9e55-cf602bc7c014","label":"a","content":"Write the following numbers in order of size.\n\nStart with the smallest number.\n\n0.15 $\\frac{1}{6}$ 16% $\\frac{1}{5}$ 0.155","markscheme":"- Converts at least 3 numbers to a common format (e.g., $0.15, 0.167, 0.16, 0.2, 0.155$) M1\n- Correct order: $0.15, 0.155, 16\\%, \\frac{1}{6}, \\frac{1}{5}$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Attempts to convert at least 3 numbers to a common format (decimals, fractions with common denominator, or percentages).","code":"M"},{"id":"p2","marks":1,"description":"Correctly orders all numbers: 0.15, 0.155, 16%, 1/6, 1/5.","code":"A"}],"finalAnswers":["$$0.15, 0.155, 16\\%, \\frac{1}{6}, \\frac{1}{5}$"],"generatedAt":"2026-05-06T13:59:15.838Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"common_format","label":"Convert to decimals","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=sixth_value}{\\frac{1}{6}}=0.1666\\ldots$"},{"latex":"$$\\htmlData{anchor=percentage_value}{16\\%}=0.16$"},{"latex":"$$\\htmlData{anchor=fifth_value}{\\frac{1}{5}}=0.2$"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"$$\\frac{1}{6}$"},{"color":"amber","style":"text-color-with-background","anchor":"16%"},{"color":"green","style":"text-color-with-background","anchor":"$$\\frac{1}{5}$"}]},"order":0,"title":"Convert the values","description":"Use decimals for all five values so they can be compared by place value. These three correct conversions earn the method mark (M1)."},{"type":"text","order":1,"title":"Compare place values","content":"Align the decimal places by adding zeros where needed:\n\n$$0.150,\\quad 0.1666\\ldots,\\quad 0.160,\\quad 0.200,\\quad 0.155$$\n\nNow compare the digits from left to right. This gives\n\n$$0.150<0.155<0.160<0.1666\\ldots<0.200.$$\n\nIn particular, $0.15=0.150$, so $0.15$ is smaller than $0.155$."},{"type":"text","order":2,"title":"Write the order","content":"Now rewrite the decimals in the sorted order using the original forms from the question:\n\n$$0.15<0.155<16\\%<\\frac{1}{6}<\\frac{1}{5}$$\n\nThe complete correct order earns the accuracy mark (A1)."}]}],"generatedAt":"2026-07-19T02:07:28.600Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":{"methods":[{"id":"decimal_comparison","label":"Decimal Comparison","steps":[{"type":"text","order":0,"title":"Identify the goal","content":"The question asks us to order five numbers from smallest to largest. To do this easily, we will convert all of them into decimals with the same number of decimal places for a direct comparison.","highlights":[{"text":"Write the following numbers in order of size.","location":"specification"},{"text":"Start with the smallest number.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$$\\htmlData{anchor=o1}{\\frac{1}{6}} = 1 \\div 6 = \\htmlData{anchor=d1}{0.166\\dots}$$"},{"latex":"$$$\\htmlData{anchor=o2}{16\\%} = \\frac{16}{100} = \\htmlData{anchor=d2}{0.160}$$"},{"latex":"$$$\\htmlData{anchor=o3}{\\frac{1}{5}} = \\frac{2}{10} = \\htmlData{anchor=d3}{0.200}$$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"o1"},{"color":"amber","style":"text-color","anchor":"o2"},{"color":"purple","style":"text-color","anchor":"o3"}],"connections":[{"to":"d1","from":"o1","color":"sky","label":"division","style":"solid"},{"to":"d2","from":"o2","color":"amber","label":"percent to decimal","style":"solid"},{"to":"d3","from":"o3","color":"purple","label":"equivalent fraction","style":"solid"}]},"order":1,"title":"Convert to decimals","description":"We convert the fractions

Fractions, Decimals and Percentages

Question 3

Fractions, Decimals and Percentages Questions

Fractions, Decimals and Percentages

Question 3

Fractions, Decimals and Percentages Questions