Converting Decimals and Fractions Cornell Notes Formatting
How to convert fractions to decimals and vice versa using long division methods with examples. Learn to express mixed numbers as decimals and understand the relationship between fractions and decimals.
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02 March 2025 Convert terminating decimals and recurring decimals to fractions LO: To correctly convert terminating decimals to fractions. To correctly convert recurring decimals to fractions. www.mathssupport.org
Writing a terminating decimal as a fraction (1) Write all the digits after the decimal point (2) Draw a line under these (3) Put a 0 under each digit (4) Put a 1 in front of the 0 s (5) Simplify if possible Examples 213 000 1 013 000 1 37 00 1 0.213 0.013 0.37 = = = 13 = 1000 www.mathssupport.org
Writing a recurring decimal as a fraction If the recurring part start straight after the decimal point, then we can express the decimal as a fraction by using methods as illustrated in the following examples: . x = 0.777777 0.7 10x = 7.777777 Multiply both sides by 10 Subtract the top from the bottom 9x = 7 9 Divide both sides by 9 9 7 9 x = www.mathssupport.org
Writing a recurring decimal as a fraction If the recurring part start straight after the decimal point, then we can express the decimal as a fraction by using methods as illustrated in the following examples: . . x = 0.383838 0.38 100x = 38.383838 Multiply both sides by 100 Subtract the top from the bottom 99x = 38 99 Divide both sides by 99 99 38 99 x = www.mathssupport.org
Writing a recurring decimal as a fraction If the recurring part start straight after the decimal point, then we can express the decimal as a fraction by using methods as illustrated in the following examples: . . x = 0.462462 1000x = 462.462462 0.462 Multiply both sides by 1000 Subtract the top from the bottom 999x = 462 999 Divide both sides by 999 999 462 999 154 333 Simplify x = x = www.mathssupport.org
Writing a recurring decimal as a fraction If the recurring part starts straight after the decimal point, then it s easy . . . Have you noticed the pattern? If the fraction has 1 recurring digit, it s that digit over 9 If the fraction has 2 recurring digits, it s those digits over 99 If the fraction has 3 recurring digits, it s those digits over 999, and so on. Examples . .. .. 38 99 462 999 7 9 0.38 0.462 0.7 = = = 154 333 = www.mathssupport.org
Writing a recurring decimal as a fraction If the recurring part doesn t start straight after the decimal point, then we can express the decimal as a fraction by using methods as illustrated in the following examples: . x = 0.733333 10x = 7.33333 0.73 Scale up the above so that recurring part starts straight after decimal point 100x = 73.3333 Scale the above to line up recurring parts Subtract the two equations above 90x = 66 90 Divide both sides by 90 90 66 90 11 15 x = = www.mathssupport.org
Writing a recurring decimal as a fraction If the recurring part doesn t start straight after the decimal point, then we can express the decimal as a fraction by using methods as illustrated in the following examples: . x = 0.588888 10x = 5.88888 0.58 Scale up the above so that recurring part starts straight after decimal point 100x = 58.8 Scale the above to line up recurring parts Subtract the two equations above 90x = 53 90 Divide both sides by 90 90 53 90 x = www.mathssupport.org
Writing a recurring decimal as a fraction If the recurring part doesn t start straight after the decimal point, then we can express the decimal as a fraction by using methods as illustrated in the following examples: .. x = 0.6585858 10x = 6.585858 1000x = 658.5858 0.658 Scale up the above so that recurring part starts straight after decimal point Scale the above to line up recurring parts Subtract the two equations above 990x = 652 990 Divide both sides by 990 990 652 990 326 495 = x = www.mathssupport.org
Writing a recurring decimal as a fraction If the recurring part doesn t start straight after the decimal point, then we can express the decimal as a fraction by using methods as illustrated in the following examples: .. x = 0.1747474 10x = 1.747474 0.174 Scale up the above so that recurring part starts straight after decimal point 1000x = 174.7474 Scale the above to line up recurring parts Subtract the two equations above 990x = 173 990 Divide both sides by 990 990 173 990 x = www.mathssupport.org
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