longmult 0.00003*58.3197

{ "query": { "display": "long multiplication $$0.00003\\cdot\\:58.3197$$", "symbolab_question": "PRE_ALGEBRA#longmult 0.00003\\cdot 58.3197" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Decimals", "subTopic": "Long Multiplication", "default": "0.001749591", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$0.00003\\cdot\\:58.3197=0.001749591$$", "input": "0.00003\\cdot\\:58.3197", "steps": [ { "type": "step", "primary": "Multiply without the decimal points, then put the decimal point in the answer" }, { "type": "interim", "title": "$$3\\cdot\\:583197=1749591$$", "input": "3\\cdot\\:583197", "steps": [ { "type": "step", "primary": "Line up the numbers", "result": "\\begin{matrix}\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&3\\\\\\times\\:&5&8&3&1&9&7\\end{matrix}" }, { "type": "step", "primary": "For convenience, place the longer number on top", "result": "583197\\cdot\\:3" }, { "type": "step", "primary": "Line up the numbers", "result": "\\begin{matrix}\\:\\:&5&8&3&1&9&7\\\\\\times\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&3\\end{matrix}" }, { "type": "step", "primary": "Multiply the top number by the bottom number one digit at a time starting with the ones digit (from right to left)" }, { "type": "step", "primary": "Mutliply the bold numbers: $$7\\cdot\\:3=21$$", "secondary": [ "Carry $$2$$ to the column on the left and write $$1$$ in the result line" ], "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&2&\\:\\:\\\\\\:\\:&5&8&3&1&9&\\bold{7}\\\\\\times\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\bold{3}\\end{matrix}}{\\begin{matrix}\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&1\\end{matrix}}" }, { "type": "step", "primary": "Add the carried number to the multiplication: $$2+9\\cdot\\:3=29$$", "secondary": [ "Carry $$2$$ to the column on the left and write $$9$$ in the result line" ], "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&\\:\\:&\\:\\:&2&\\bold{2}&\\:\\:\\\\\\:\\:&5&8&3&1&\\bold{9}&7\\\\\\times\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\bold{3}\\end{matrix}}{\\begin{matrix}\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&9&1\\end{matrix}}" }, { "type": "step", "primary": "Add the carried number to the multiplication: $$2+1\\cdot\\:3=5$$", "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\bold{2}&2&\\:\\:\\\\\\:\\:&5&8&3&\\bold{1}&9&7\\\\\\times\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\bold{3}\\end{matrix}}{\\begin{matrix}\\:\\:&\\:\\:&\\:\\:&\\:\\:&5&9&1\\end{matrix}}" }, { "type": "step", "primary": "Mutliply the bold numbers: $$3\\cdot\\:3=9$$", "result": "\\frac{\\begin{matrix}\\:\\:&\\:\\:&\\:\\:&\\:\\:&2&2&\\:\\:\\\\\\:\\:&5&8&\\bold{3}&1&9&7\\\\\\times\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\bold{3}\\end{matrix}}{\\begin{matrix}\\:\\:&\\:\\:&\\:\\:&9&5&9&1\\end{matrix}}" }, { "type": "step", "primary": "Mutliply the bold numbers: $$8\\cdot\\:3=24$$", "secondary": [ "Carry $$2$$ to the column on the left and write $$4$$ in the result line" ], "result": "\\frac{\\begin{matrix}\\:\\:&2&\\:\\:&\\:\\:&2&2&\\:\\:\\\\\\:\\:&5&\\bold{8}&3&1&9&7\\\\\\times\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\bold{3}\\end{matrix}}{\\begin{matrix}\\:\\:&\\:\\:&4&9&5&9&1\\end{matrix}}" }, { "type": "step", "primary": "Add the carried number to the multiplication: $$2+5\\cdot\\:3=17$$", "secondary": [ "Carry $$1$$ to the column on the left and write $$7$$ in the result line" ], "result": "\\frac{\\begin{matrix}\\:\\:&1&\\bold{2}&\\:\\:&\\:\\:&2&2&\\:\\:\\\\\\:\\:&\\:\\:&\\bold{5}&8&3&1&9&7\\\\\\times\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\bold{3}\\end{matrix}}{\\begin{matrix}\\:\\:&\\:\\:&7&4&9&5&9&1\\end{matrix}}" }, { "type": "step", "primary": "Add the carried digit, $$1$$, to the result", "result": "\\frac{\\begin{matrix}\\:\\:&1&2&\\:\\:&\\:\\:&2&2&\\:\\:\\\\\\:\\:&\\:\\:&5&8&3&1&9&7\\\\\\times\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&\\:\\:&3\\end{matrix}}{\\begin{matrix}\\:\\:&1&7&4&9&5&9&1\\end{matrix}}" }, { "type": "step", "result": "=1749591" } ], "meta": { "interimType": "N/A" } }, { "type": "step", "primary": "$$0.00003$$ has $$5$$ decimal places", "secondary": [ "$$58.3197$$ has $$4$$ decimal places", "Therefore, the answer has $$9$$ decimal places" ], "result": "=0.001749591" } ], "meta": { "solvingClass": "StepsLongMultiplication" } }, "meta": { "showVerify": true } }