During a maths lesson Mary worked out a question and got the answer as 1.8i recurring. Convert into a…

Question

During a maths lesson Mary worked out a question and got the answer as 1.8i recurring. Convert into a fraction (let 1.8i to be x)

ScanSolve AI Tutor · Accepted Answer

Step 1: Set the given recurring decimal equal to x. The notation 1.81 means 1.8111.... x = 1.8111... (1) Step 2: Multiply equation (1) by 10 to move the non-recurring digit to the left of the decimal point. 10x = 18.111... (2) Step 3: Multiply equation (1) by 100 to move one full recurring block (including the non-recurring part) to the left of the decimal point. 100x = 181.111... (3) Step 4: Subtract equation (2) from equation (3) to eliminate the recurring part. 100x − 10x = 181.111... − 18.111... 90x = 163 Step 5: Solve for x by dividing both sides by 90. x = 163/90 The fraction is already in its simplest form since 163 is a prime number and 90 is not a multiple of 163. The final answer is 163/90.

During a maths lesson Mary worked out a question and got the answer as 1.8i recurring. Convert into a fraction (let 1.8i to be x)

Answer

Step-by-step solution

Set the given recurring decimal equal to $x$ .

Multiply equation (1) by 10 to move the non-recurring digit to the left of the decimal point.

Multiply equation (1) by 100 to move one full recurring block (including the non-recurring part) to the left of the decimal point.

Subtract equation (2) from equation (3) to eliminate the recurring part.

Solve for $x$ by dividing both sides by 90.

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More Mathematics Questions

During a maths lesson Mary worked out a question and got the answer as 1.8i recurring. Convert into a fraction (let 1.8i to be x)

Answer

Step-by-step solution

Set the given recurring decimal equal to xxx.

Multiply equation (1) by 10 to move the non-recurring digit to the left of the decimal point.

Multiply equation (1) by 100 to move one full recurring block (including the non-recurring part) to the left of the decimal point.

Subtract equation (2) from equation (3) to eliminate the recurring part.

Solve for xxx by dividing both sides by 90.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Set the given recurring decimal equal to $x$ .

Solve for $x$ by dividing both sides by 90.