dectofrac 3.2

{ "query": { "display": "decimal to fraction $$3.2$$", "symbolab_question": "PRE_ALGEBRA#dectofrac 3.2" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Decimals", "subTopic": "Decimals to Fraction", "default": "3\\frac{1}{5}", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Convert $$3.2$$ to a fraction:$${\\quad}3\\frac{1}{5}$$", "input": "3.2", "steps": [ { "type": "step", "primary": "Rewrite as", "result": "=3+0.2" }, { "type": "interim", "title": "Convert $$0.2$$ to a fraction:$${\\quad}\\frac{1}{5}$$", "input": "0.2", "steps": [ { "type": "step", "primary": "Multiply and divide by 10 for every number after the decimal point<br/>There is $$1$$ digit to the right of the decimal point, therefore multiply and divide by $$10$$", "result": "=\\frac{0.2\\cdot\\:10}{10}" }, { "type": "step", "result": "=\\frac{2}{10}" }, { "type": "interim", "title": "Reduce the fraction $$\\frac{2}{10}:{\\quad}\\frac{1}{5}$$", "input": "\\frac{2}{10}", "steps": [ { "type": "step", "primary": "Find a common factor of $$2$$ and $$10$$ in order to cancel it out " }, { "type": "interim", "title": "Greatest Common Divisor of $$2,\\:10:{\\quad}2$$", "input": "2,\\:10", "steps": [ { "type": "definition", "title": "Greatest Common Divisor (GCD)", "text": "The GCD of $$a,\\:b$$ is the largest positive number that divides both $$a$$ and $$b$$ without a remainder" }, { "type": "interim", "title": "Prime factorization of $$2:{\\quad}2$$", "input": "2", "steps": [ { "type": "step", "primary": "$$2$$ is a prime number, therefore no factorization is possible", "result": "=2" } ], "meta": { "solvingClass": "Composite Integer", "interimType": "Prime Fac 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMrfn8NOj0LUzuzje6xTyxRl8ZboA8wPLg0yhI4RzfjFw/y9DKGIPglJ+qMi9xDu2KE1OovxZAaXg7BtrFPk4UcCzRnGgMN6CYRfod7Mq0dp1+G9v2aKasChgV65VW8cTW" } }, { "type": "interim", "title": "Prime factorization of $$10:{\\quad}2\\cdot\\:5$$", "input": "10", "steps": [ { "type": "step", "primary": "$$10\\:$$divides by $$2\\quad\\:10=5\\cdot\\:2$$", "result": "=2\\cdot\\:5" }, { "type": "step", "primary": "$$2,\\:5$$ are all prime numbers, therefore no further factorization is possible", "result": "=2\\cdot\\:5" } ], "meta": { "solvingClass": "Composite Integer", "interimType": "Prime Fac 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMrfn8NOj0LUzuzje6xTyxRvTIRluRNPwUULD5JCqpmdzwPjJo8Fi+uo29zEltAtWEB4gitN/2ICkrV6ivfiR3BLFRzd4QlsM8ugKm4vxBIEBeUcq3/p8vCxgx1MIzcdLE" } }, { "type": "step", "primary": "The prime factors common to $$2,\\:10$$ are ", "result": "=2" } ], "meta": { "solvingClass": "GCD", "interimType": "GCD Top 1Eq" } }, { "type": "step", "primary": "Factor out $$2$$ from the numerator and the denominator<br/>$$2=2\\cdot\\:1,\\:{\\quad}10=2\\cdot\\:5$$", "result": "=\\frac{2\\cdot\\:1}{2\\cdot\\:5}" }, { "type": "step", "primary": "Cancel the common factor: $$2$$", "result": "=\\frac{1}{5}" } ], "meta": { "interimType": "Reduce Fraction 1Eq" } }, { "type": "step", "result": "=\\frac{1}{5}" } ], "meta": { "interimType": "Convert To Fraction 1Eq" } }, { "type": "step", "result": "=3+\\frac{1}{5}" }, { "type": "step", "result": "=3\\frac{1}{5}" } ], "meta": { "solvingClass": "decToFrac" } }, "meta": { "showVerify": true } }