dectofrac 0.252

{ "query": { "display": "decimal to fraction $$0.252$$", "symbolab_question": "PRE_ALGEBRA#dectofrac 0.252" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Decimals", "subTopic": "Decimals to Fraction", "default": "\\frac{63}{250}", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Convert $$0.252$$ to a fraction:$${\\quad}\\frac{63}{250}$$", "input": "0.252", "steps": [ { "type": "step", "primary": "Multiply and divide by 10 for every number after the decimal point.<br/>There are $$3$$ digits to the right of the decimal point, therefore multiply and divide by $$1000$$", "result": "=\\frac{0.252\\cdot\\:1000}{1000}" }, { "type": "step", "result": "=\\frac{252}{1000}" }, { "type": "interim", "title": "Reduce the fraction $$\\frac{252}{1000}:{\\quad}\\frac{63}{250}$$", "input": "\\frac{252}{1000}", "steps": [ { "type": "step", "primary": "Find a common factor of $$252$$ and $$1000$$ in order to cancel it out " }, { "type": "interim", "title": "Greatest Common Divisor of $$252,\\:1000:{\\quad}4$$", "input": "252,\\:1000", "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 $$252:{\\quad}2\\cdot\\:2\\cdot\\:3\\cdot\\:3\\cdot\\:7$$", "input": "252", "steps": [ { "type": "step", "primary": "$$252\\:$$divides by $$2\\quad\\:252=126\\cdot\\:2$$", "result": "=2\\cdot\\:126" }, { "type": "step", "primary": "$$126\\:$$divides by $$2\\quad\\:126=63\\cdot\\:2$$", "result": "=2\\cdot\\:2\\cdot\\:63" }, { "type": "step", "primary": "$$63\\:$$divides by $$3\\quad\\:63=21\\cdot\\:3$$", "result": "=2\\cdot\\:2\\cdot\\:3\\cdot\\:21" }, { "type": "step", "primary": "$$21\\:$$divides by $$3\\quad\\:21=7\\cdot\\:3$$", "result": "=2\\cdot\\:2\\cdot\\:3\\cdot\\:3\\cdot\\:7" }, { "type": "step", "primary": "$$2,\\:3,\\:7$$ are all prime numbers, therefore no further factorization is possible", "result": "=2\\cdot\\:2\\cdot\\:3\\cdot\\:3\\cdot\\:7" } ], "meta": { "solvingClass": "Composite Integer", "interimType": "Prime Fac 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMrfn8NOj0LUzuzje6xTyxRl8ZboA8wPLg0yhI4RzfjFyt9ksHkMhjJvGmfig1B6RY9NqQ+lATTQCpcI1REFC/BKGFkX1ACFJO8XX3CmdEmA0gqIj+e6OmhFSG2+J1VkeD" } }, { "type": "interim", "title": "Prime factorization of $$1000:{\\quad}2\\cdot\\:2\\cdot\\:2\\cdot\\:5\\cdot\\:5\\cdot\\:5$$", "input": "1000", "steps": [ { "type": "step", "primary": "$$1000\\:$$divides by $$2\\quad\\:1000=500\\cdot\\:2$$", "result": "=2\\cdot\\:500" }, { "type": "step", "primary": "$$500\\:$$divides by $$2\\quad\\:500=250\\cdot\\:2$$", "result": "=2\\cdot\\:2\\cdot\\:250" }, { "type": "step", "primary": "$$250\\:$$divides by $$2\\quad\\:250=125\\cdot\\:2$$", "result": "=2\\cdot\\:2\\cdot\\:2\\cdot\\:125" }, { "type": "step", "primary": "$$125\\:$$divides by $$5\\quad\\:125=25\\cdot\\:5$$", "result": "=2\\cdot\\:2\\cdot\\:2\\cdot\\:5\\cdot\\:25" }, { "type": "step", "primary": "$$25\\:$$divides by $$5\\quad\\:25=5\\cdot\\:5$$", "result": "=2\\cdot\\:2\\cdot\\:2\\cdot\\:5\\cdot\\:5\\cdot\\:5" }, { "type": "step", "primary": "$$2,\\:5$$ are all prime numbers, therefore no further factorization is possible", "result": "=2\\cdot\\:2\\cdot\\:2\\cdot\\:5\\cdot\\:5\\cdot\\:5" } ], "meta": { "solvingClass": "Composite Integer", "interimType": "Prime Fac 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMrfn8NOj0LUzuzje6xTyxRvTIRluRNPwUULD5JCqpmdx6u/W5X82u+9iIzxwjGh4W+ZE2CuWYXhz/1zRh+DBwSWJYgvXjl1/GaaWGY6UA4hEupxz5HyJJqI1wKMfaMDcJ" } }, { "type": "step", "primary": "The prime factors common to $$252,\\:1000$$ 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/>$$252=4\\cdot\\:63,\\:{\\quad}1000=4\\cdot\\:250$$", "result": "=\\frac{4\\cdot\\:63}{4\\cdot\\:250}" }, { "type": "step", "primary": "Cancel the common factor: $$4$$", "result": "=\\frac{63}{250}" } ], "meta": { "interimType": "Reduce Fraction 1Eq" } }, { "type": "step", "result": "=\\frac{63}{250}" } ], "meta": { "solvingClass": "decToFrac" } }, "meta": { "showVerify": true } }