n\n$$420 \\times 10^{-5}$$\n\n$$42 \\times 10^{-1}$$","markscheme":"- Converts all to ordinary numbers: 0.042, 0.42, 0.0042, 4.2 M1\n- Correct order: $420 \\times 10^{-5}$, $4.2 \\times 10^{-2}$, $0.0042 \\times 10^2$, $42 \\times 10^{-1}$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Converts at least three numbers to a common form (e.g., ordinary numbers: 0.042, 0.42, 0.0042, 4.2) or standard form.","code":"M"},{"id":"p2","marks":1,"description":"Correctly orders the original numbers: $420 \\times 10^{-5}$, $4.2 \\times 10^{-2}$, $0.0042 \\times 10^2$, $42 \\times 10^{-1}$.","code":"A"}],"finalAnswers":["$$420 \\times 10^{-5}, 4.2 \\times 10^{-2}, 0.0042 \\times 10^2, 42 \\times 10^{-1}$"],"generatedAt":"2026-05-06T14:06:40.968Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"convert_and_compare","label":"Convert and compare","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$4.2\\times 10^{-2}=0.042$"},{"latex":"$$0.0042\\times 10^{2}=0.42$"},{"latex":"$$420\\times 10^{-5}=0.0042$"},{"latex":"$$42\\times 10^{-1}=4.2$"}]},"order":1,"title":"Move decimal points","description":"A negative power of 10 moves the decimal point to the left, while a positive power moves it to the right. Converting all four expressions to ordinary decimals earns the method mark, even if the final ordering later slips."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=decimal_order}{0.0042 < 0.042 < 0.42 < 4.2}$"},{"latex":"$$\\htmlData{anchor=original_order}{420 \\times 10^{-5} < 4.2 \\times 10^{-2} < 0.0042 \\times 10^{2} < 42 \\times 10^{-1}}$"}],"connections":[{"to":"original_order","from":"decimal_order","color":"green","label":"use matching order","style":"solid"}]},"order":2,"title":"Order the decimals","description":"The converted decimals increase from left to right. Now write the original expressions in that same order to earn the accuracy mark."}]}],"generatedAt":"2026-07-19T18:52:54.123Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":{"methods":[{"id":"decimalconversion","label":"Decimal Conversion","steps":[{"type":"text","order":0,"title":"Identify the approach","content":"To order these numbers correctly, we will convert each one from scientific notation or power-of-10 form into a standard decimal number. This makes it much easier to compare their actual sizes."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=val1}{4.2 \\times 10^{-2}}$"},{"latex":"$$\\htmlData{anchor=res1}{0.042}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"val1"},{"color":"sky","style":"text-color","anchor":"res1"}],"connections":[{"to":"res1","from":"val1","color":"sky","label":"2 places left","style":"solid"}]},"order":1,"title":"Convert the first number","description":"For $4.2 \\times 10^{-2}$, the negative power means we move the decimal point 2 places to the left."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=val2}{0.0042 \\times 10^2}$"},{"latex":"$$\\htmlData{anchor=res2}{0.42}$"}],"highlights":[{"color":"amber","style":"text-color","anchor":"val2"},{"color":"amber","style":"text-color","anchor":"res2"}],"connections":[{"to":"res2","from":"val2","color":"amber","label":"2 places right","style":"solid"}]},"order":2,"title":"Convert the second number","description":"For $0.0042 \\times 10^2$, the positive power means we move the decimal point 2 places to the right."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=val3}{420 \\times 10^{-5}}$"},{"latex":"$$\\htmlData{anchor=res3}{0.0042}$"}],"highlights":[{"color":"purple","style":"text-color","anchor":"val3"},{"color":"purple","style":"text-color","anchor":"res3"}],"connections":[{"to":"res3","from":"val3","color":"purple","label":"5 places left","style":"solid"}]},"order":3,"title":"Convert the third number","description":"For $420 \\times 10^{-5}$, we move the decimal point (starting after the zero) 5 places to the left."

Standard Form Questions

Standard Form Questions

Standard Form Questions

Standard Form Questions