{
"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
}
}
Solution
long multiplication
Solution
Solution steps
Multiply without the decimal points, then put the decimal point in the answer
Line up the numbers
For convenience, place the longer number on top
Line up the numbers
Multiply the top number by the bottom number one digit at a time starting with the ones digit (from right to left)
Mutliply the bold numbers: Carry to the column on the left and write in the result line
Add the carried number to the multiplication: Carry to the column on the left and write in the result line
Add the carried number to the multiplication:
Mutliply the bold numbers:
Mutliply the bold numbers: Carry to the column on the left and write in the result line
Add the carried number to the multiplication: Carry to the column on the left and write in the result line
Add the carried digit, , to the result
has decimal places has decimal places
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Frequently Asked Questions (FAQ)
What is longmult 0.00003*58.3197 ?
The solution to longmult 0.00003*58.3197 is 0.001749591
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