fractodec 7/8

{ "query": { "display": "fraction to decimal $$\\frac{7}{8}$$", "symbolab_question": "PRE_ALGEBRA#fractodec \\frac{7}{8}" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Decimals", "subTopic": "Fraction to Decimals", "default": "0.875", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Convert to decimal $$\\frac{7}{8}:{\\quad}0.875$$", "steps": [ { "type": "step", "primary": "Convert $$\\frac{7}{8}\\:$$to decimal by applying long division" }, { "type": "interim", "title": "Long Division $$\\frac{7}{8}:{\\quad}0.875$$", "input": "\\frac{7}{8}", "steps": [ { "type": "interim", "title": "Divide $$7\\:$$by $$8\\:$$to get $$0$$", "input": "\\:", "result": "\\begin{array}{l}\\:\\:\\:\\:0.\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\8\\overline{|\\kern0.1em7.0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:70\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\end{array}", "steps": [ { "type": "step", "primary": "Divide $$7\\:$$by $$8\\:$$to get $$0$$", "result": "\\begin{array}{l}\\:\\:\\:\\:0\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\8\\overline{|\\kern0.1em7}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\end{array}" }, { "type": "step", "primary": "Multiply the quotient digit $$\\left(0\\right)\\:$$by the divisor $$8$$", "result": "\\begin{array}{l}\\:\\:\\:\\:0\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\8\\overline{|\\kern0.1em7}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\end{array}" }, { "type": "step", "primary": "Subtract $$0\\:$$from $$7$$", "result": "\\begin{array}{l}\\:\\:\\:\\:0\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\8\\overline{|\\kern0.1em7}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:7\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\end{array}" }, { "type": "step", "primary": "Add a decimal place and a zero to the dividend", "secondary": [ "Bring down the zero from the dividend" ], "result": "\\begin{array}{l}\\:\\:\\:\\:0.\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\8\\overline{|\\kern0.1em7.0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:70\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\end{array}" } ], "meta": { "interimType": "Long Division Divide 3Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjAuRbUqF0v2PpVuPGQH4dLbLeu+MH3/4O31zRKyMpNuXtAM4L+5fXXw9GSOcy6r1711oAtzvW4Xq9Ydy3xV9wb7zP7ovb9THepx85Rpn8irs7nxrODmx8dzZSf6H8RiCJbxuDg/SIylxapO2ETW8RZCoDf0fGF27xbfjZp+N8nz/44V7GaPzKCvkEVvnnf/0yo=" } }, { "type": "interim", "title": "Divide $$70\\:$$by $$8\\:$$to get $$8$$", "input": "\\:", "result": "\\begin{array}{l}\\:\\:\\:\\:0.8\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\8\\overline{|\\kern0.1em7.00}\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:70\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{64}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:60\\:\\:\\:\\:\\:\\:\\:\\:\\end{array}", "steps": [ { "type": "step", "primary": "Divide $$70\\:$$by $$8\\:$$to get $$8$$", "result": "\\begin{array}{l}\\:\\:\\:\\:0.8\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\8\\overline{|\\kern0.1em7.0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:70\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\end{array}" }, { "type": "step", "primary": "Multiply the quotient digit $$\\left(8\\right)\\:$$by the divisor $$8$$", "result": "\\begin{array}{l}\\:\\:\\:\\:0.8\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\8\\overline{|\\kern0.1em7.0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:70\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{64}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\end{array}" }, { "type": "step", "primary": "Subtract $$64\\:$$from $$70$$", "result": "\\begin{array}{l}\\:\\:\\:\\:0.8\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\8\\overline{|\\kern0.1em7.0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:70\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{64}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:6\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\end{array}" }, { "type": "step", "primary": "Add a zero to the dividend", "secondary": [ "Bring down the zero from the dividend" ], "result": "\\begin{array}{l}\\:\\:\\:\\:0.8\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\8\\overline{|\\kern0.1em7.00}\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:70\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{64}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:60\\:\\:\\:\\:\\:\\:\\:\\:\\end{array}" } ], "meta": { "interimType": "Long Division Divide 3Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjAuRbUqF0v2PpVuPGQH4dLbLeu+MH3/4O31zRKyMpNuXtAM4L+5fXXw9GSOcy6r170F1bMyRAJ/Zn9FpXvOBI8YJhhOUJ4+b0sozmBJodb1hZEQlrQ67quu86RDujFLtS5FcjWKRqLhvxEi4F5kztDTTSgIVB+5WX9U9YExfSYyGR3Z7lLRz+FS/MwAm7CZoks=" } }, { "type": "interim", "title": "Divide $$60\\:$$by $$8\\:$$to get $$7$$", "input": "\\:", "result": "\\begin{array}{l}\\:\\:\\:\\:0.87\\:\\:\\:\\:\\:\\:\\:\\\\8\\overline{|\\kern0.1em7.000}\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:70\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{64}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:60\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:\\underline{56}\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:\\:\\:40\\:\\:\\:\\:\\:\\:\\end{array}", "steps": [ { "type": "step", "primary": "Divide $$60\\:$$by $$8\\:$$to get $$7$$", "result": "\\begin{array}{l}\\:\\:\\:\\:0.87\\:\\:\\:\\:\\:\\:\\:\\\\8\\overline{|\\kern0.1em7.00}\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:70\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{64}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:60\\:\\:\\:\\:\\:\\:\\:\\:\\end{array}" }, { "type": "step", "primary": "Multiply the quotient digit $$\\left(7\\right)\\:$$by the divisor $$8$$", "result": "\\begin{array}{l}\\:\\:\\:\\:0.87\\:\\:\\:\\:\\:\\:\\:\\\\8\\overline{|\\kern0.1em7.00}\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:70\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{64}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:60\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:\\underline{56}\\:\\:\\:\\:\\:\\:\\:\\:\\end{array}" }, { "type": "step", "primary": "Subtract $$56\\:$$from $$60$$", "result": "\\begin{array}{l}\\:\\:\\:\\:0.87\\:\\:\\:\\:\\:\\:\\:\\\\8\\overline{|\\kern0.1em7.00}\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:70\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{64}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:60\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:\\underline{56}\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:\\:\\:4\\:\\:\\:\\:\\:\\:\\:\\:\\end{array}" }, { "type": "step", "primary": "Add a zero to the dividend", "secondary": [ "Bring down the zero from the dividend" ], "result": "\\begin{array}{l}\\:\\:\\:\\:0.87\\:\\:\\:\\:\\:\\:\\:\\\\8\\overline{|\\kern0.1em7.000}\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:70\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{64}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:60\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:\\underline{56}\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:\\:\\:40\\:\\:\\:\\:\\:\\:\\end{array}" } ], "meta": { "interimType": "Long Division Divide 3Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjAuRbUqF0v2PpVuPGQH4dLbLeu+MH3/4O31zRKyMpNuXtAM4L+5fXXw9GSOcy6r172Kt/fXW6GtZs6KXdGfVNY5DtpcmEplXAySADBvNzqdrZEQlrQ67quu86RDujFLtS45iPtFOWexaVNfcwdbXg+gTSgIVB+5WX9U9YExfSYyGWWq+UEXbxIwdsY2WyhLQTQ=" } }, { "type": "interim", "title": "Divide $$40\\:$$by $$8\\:$$to get $$5$$", "input": "\\:", "result": "\\begin{array}{l}\\:\\:\\:\\:0.875\\:\\:\\:\\:\\:\\\\8\\overline{|\\kern0.1em7.000}\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:70\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{64}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:60\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:\\underline{56}\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:\\:\\:40\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:\\:\\:\\underline{40}\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:0\\:\\:\\:\\:\\:\\:\\end{array}", "steps": [ { "type": "step", "primary": "Divide $$40\\:$$by $$8\\:$$to get $$5$$", "result": "\\begin{array}{l}\\:\\:\\:\\:0.875\\:\\:\\:\\:\\:\\\\8\\overline{|\\kern0.1em7.000}\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:70\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{64}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:60\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:\\underline{56}\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:\\:\\:40\\:\\:\\:\\:\\:\\:\\end{array}" }, { "type": "step", "primary": "Multiply the quotient digit $$\\left(5\\right)\\:$$by the divisor $$8$$", "result": "\\begin{array}{l}\\:\\:\\:\\:0.875\\:\\:\\:\\:\\:\\\\8\\overline{|\\kern0.1em7.000}\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:70\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{64}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:60\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:\\underline{56}\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:\\:\\:40\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:\\:\\:\\underline{40}\\:\\:\\:\\:\\:\\:\\end{array}" }, { "type": "step", "primary": "Subtract $$40\\:$$from $$40$$", "result": "\\begin{array}{l}\\:\\:\\:\\:0.875\\:\\:\\:\\:\\:\\\\8\\overline{|\\kern0.1em7.000}\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{0}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:70\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\underline{64}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:60\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:\\underline{56}\\:\\:\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:\\:\\:40\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:\\:\\:\\underline{40}\\:\\:\\:\\:\\:\\:\\\\\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:0\\:\\:\\:\\:\\:\\:\\end{array}" } ], "meta": { "interimType": "Long Division Divide 3Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjAuRbUqF0v2PpVuPGQH4dLbLeu+MH3/4O31zRKyMpNuXtAM4L+5fXXw9GSOcy6r173hbgO07nM8hTELc1HxU76CwaAFKIpvcBUn7FI5c7iJAZEQlrQ67quu86RDujFLtS65VYYtgWmHUv35vI2xwRadTSgIVB+5WX9U9YExfSYyGQk9x7opyzXsvG89cdN6nqU=" } }, { "type": "step", "primary": "The solution for Long Division of $$\\frac{7}{8}\\:$$is $$0.875$$", "result": "0.875" } ], "meta": { "solvingClass": "StepsLongDivisionDecimals", "interimType": "Long Division Title 1Eq" } }, { "type": "step", "result": "0.875" } ] }, "meta": { "showVerify": true } }