compute the sum of .5 repeating and Question

Question

compute the sum of .5 repeating and .194 with the 4 repeating

sanchay · Answer

the sum of repeating decimals can be found by converting them into fractions and adding them. the detailed solution and final answer is given in the attachment.

satis · Answer

let x = 0.55555.... and y = 0.19444...first we have to eliminate the repeating parts. x = 0.55555.... 10x = 5.5555...10x - x = 5.5555... - 0.5555.... or 9x = 5or x = 5/9y = 0.19444...10y = 1.944444...10y - y =  1.944444... -  0.19444...or 9y = 1.75or y = 1.75 /9x + y = 5/9 + 1.75/9 = (5+1.75)/9 = 6.75/9 = 0.75therefore, the sum of the repeating decimals 0.555... and 0.19444... is 0.75.

aymaneba · Answer

to calculate the sum of 0.5555... (repeating 5) and 0.1944... (repeating 94), we need to express these repeating decimals as fractions.

converting 0.5555... to a fraction:0.5555... is essentially 0.5 + 0.05 + 0.005 + 0.0005 + ...this can be represented as a geometric series with the first term a = 0.5 and common ratio r = 0.1.the sum of an infinite geometric series is given by s = a / (1 - r).substituting a = 0.5 and r = 0.1, we get s = 0.5 / (1 - 0.1) = 0.5 / 0.9 = 5/9.converting 0.1944... to a fraction:0.1944... is 0.19 + 0.0044 + 0.000044 + ...to express this as a geometric series, consider 0.0044...0.0044... is 0.004 + 0.0004 + 0.000004 + ...this is a geometric series with the first term a = 0.004 and common ratio r = 0.1.the sum of this series is s = a / (1 - r) = 0.004 / (1 - 0.1) = 0.004 / 0.9 = 4/900.therefore, 0.1944... is 0.19 + 4/900.calculating the sum:now, sum these two fractions: 5/9 + 0.19 + 4/900.the calculation gives us 0.75 as the sum. therefore, when these two repeating decimals are added together, the total is 0.75.

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compute the sum of .5 repeating and Question

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