<Dd> 1523 / 10000 + 987 / 9990000 = 1522464 / 9990000 </Dd> <P> Alternatively, algebra can be used, such as below: </P> <Ol> <Li> Let x = the repeating decimal: <Dl> <Dd> x = 0.1523 987 </Dd> </Dl> </Li> <Li> Multiply both sides by the power of 10 just great enough (in this case 10) to move the decimal point just before the repeating part of the decimal number: <Dl> <Dd> 10,000 x = 1,523. 987 </Dd> </Dl> </Li> <Li> Multiply both sides by the power of 10 (in this case 10) that is the same as the number of places that repeat: <Dl> <Dd> 10,000,000 x = 1,523,987. 987 </Dd> </Dl> </Li> <Li> Subtract the two equations from each other (if a = b and c = d, then a − c = b − d): <Dl> <Dd> 10,000,000 x − 10,000 x = 1,523,987. 987 − 1,523. 987 </Dd> </Dl> </Li> <Li> Continue the subtraction operation to clear the repeating decimal: <Dl> <Dd> 9,990,000 x = 1,523,987 − 1,523 </Dd> <Dd> 9,990,000 x = 1,522,464 </Dd> </Dl> </Li> <Li> Divide both sides to represent x as a fraction <Dl> <Dd> x = 1522464 / 9990000 </Dd> </Dl> </Li> </Ol> <Li> Let x = the repeating decimal: <Dl> <Dd> x = 0.1523 987 </Dd> </Dl> </Li>

Ten less than a number is equal to the same number divided by 2