dectofrac 0.36

{ "query": { "display": "decimal to fraction $$0.36$$", "symbolab_question": "PRE_ALGEBRA#dectofrac 0.36" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Decimals", "subTopic": "Decimals to Fraction", "default": "\\frac{9}{25}", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Convert $$0.36$$ to a fraction:$${\\quad}\\frac{9}{25}$$", "input": "0.36", "steps": [ { "type": "step", "primary": "Multiply and divide by 10 for every number after the decimal point.<br/>There are $$2$$ digits to the right of the decimal point, therefore multiply and divide by $$100$$", "result": "=\\frac{0.36\\cdot\\:100}{100}" }, { "type": "step", "result": "=\\frac{36}{100}" }, { "type": "interim", "title": "Reduce the fraction $$\\frac{36}{100}:{\\quad}\\frac{9}{25}$$", "input": "\\frac{36}{100}", "steps": [ { "type": "step", "primary": "Find a common factor of $$36$$ and $$100$$ in order to cancel it out " }, { "type": "interim", "title": "Greatest Common Divisor of $$36,\\:100:{\\quad}4$$", "input": "36,\\:100", "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 $$36:{\\quad}2\\cdot\\:2\\cdot\\:3\\cdot\\:3$$", "input": "36", "steps": [ { "type": "step", "primary": "$$36\\:$$divides by $$2\\quad\\:36=18\\cdot\\:2$$", "result": "=2\\cdot\\:18" }, { "type": "step", "primary": "$$18\\:$$divides by $$2\\quad\\:18=9\\cdot\\:2$$", "result": "=2\\cdot\\:2\\cdot\\:9" }, { "type": "step", "primary": "$$9\\:$$divides by $$3\\quad\\:9=3\\cdot\\:3$$", "result": "=2\\cdot\\:2\\cdot\\:3\\cdot\\:3" }, { "type": "step", "primary": "$$2,\\:3$$ are all prime numbers, therefore no further factorization is possible", "result": "=2\\cdot\\:2\\cdot\\:3\\cdot\\:3" } ], "meta": { "solvingClass": "Composite Integer", "interimType": "Prime Fac 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMrfn8NOj0LUzuzje6xTyxRlqnfsqoQ6VBiS8EyG3E6Oe5Ljmr36t3AP8UKimRmJwFB4gitN/2ICkrV6ivfiR3BLFRzd4QlsM8ugKm4vxBIEDsKDpdPajKSTz6iKfem7kI" } }, { "type": "interim", "title": "Prime factorization of $$100:{\\quad}2\\cdot\\:2\\cdot\\:5\\cdot\\:5$$", "input": "100", "steps": [ { "type": "step", "primary": "$$100\\:$$divides by $$2\\quad\\:100=50\\cdot\\:2$$", "result": "=2\\cdot\\:50" }, { "type": "step", "primary": "$$50\\:$$divides by $$2\\quad\\:50=25\\cdot\\:2$$", "result": "=2\\cdot\\:2\\cdot\\:25" }, { "type": "step", "primary": "$$25\\:$$divides by $$5\\quad\\:25=5\\cdot\\:5$$", "result": "=2\\cdot\\:2\\cdot\\:5\\cdot\\:5" }, { "type": "step", "primary": "$$2,\\:5$$ are all prime numbers, therefore no further factorization is possible", "result": "=2\\cdot\\:2\\cdot\\:5\\cdot\\:5" } ], "meta": { "solvingClass": "Composite Integer", "interimType": "Prime Fac 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMrfn8NOj0LUzuzje6xTyxRvTIRluRNPwUULD5JCqpmdz+xXOgPLRmeK8nk3Fl2YD89NqQ+lATTQCpcI1REFC/BKGFkX1ACFJO8XX3CmdEmA1u+4rbkEmrbXE7mWssOG5N" } }, { "type": "step", "primary": "The prime factors common to $$36,\\:100$$ are ", "result": "=2\\cdot\\:2" }, { "type": "step", "primary": "Multiply the numbers: $$2\\cdot\\:2=4$$", "result": "=4" } ], "meta": { "solvingClass": "GCD", "interimType": "GCD Top 1Eq" } }, { "type": "step", "primary": "Factor out $$4$$ from the numerator and the denominator<br/>$$36=4\\cdot\\:9,\\:{\\quad}100=4\\cdot\\:25$$", "result": "=\\frac{4\\cdot\\:9}{4\\cdot\\:25}" }, { "type": "step", "primary": "Cancel the common factor: $$4$$", "result": "=\\frac{9}{25}" } ], "meta": { "interimType": "Reduce Fraction 1Eq" } }, { "type": "step", "result": "=\\frac{9}{25}" } ], "meta": { "solvingClass": "decToFrac" } }, "meta": { "showVerify": true } }