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Ted is trying to change 0.4\overline{3} to a fraction - Edexcel - GCSE Maths - Question 14 - 2021 - Paper 1
Question 14
Ted is trying to change 0.4\overline{3} to a fraction. Here is the start of his method. x = 0.4\overline{3} 10x = 4.3\overline{4} Evaluate Ted's method so far.
Worked Solution & Example Answer:Ted is trying to change 0.4\overline{3} to a fraction - Edexcel - GCSE Maths - Question 14 - 2021 - Paper 1
Step 1
x = 0.4\overline{3}
Answer
To convert the repeating decimal to a fraction, we can follow these steps:
- Let ( x = 0.4\overline{3} ).
- Multiply both sides of the equation by 10 to shift the decimal point: ( 10x = 4.3\overline{3} ).
- The next step is to subtract the original ( x ) from this new equation to eliminate the repeating part: [ 10x - x = 4.3\overline{3} - 0.4\overline{3} ] This gives us ( 9x = 4.3 - 0.4 = 3.9 ).
- Notice that I have successfully eliminated the repeating decimal by aligning the subtraction. The next step would be to simplify ( 3.9 ) and then divide by 9.
Step 2
10x = 4.3\overline{4}
Answer
However, Ted made an error here as he stated ( 10x = 4.3\overline{4} ), which implies that the repeating decimal has changed. The correct step should have kept the repeating decimal consistent between initial and multiplied equations. Hence, the exact repeating sequence must remain the same in both cases, confirming that the initial alignment is crucial for accurate depiction of these values.
Step 3
Evaluate Ted's method so far.
Answer
In summary, Ted should have started over by ensuring he referenced ( 0.4\overline{3} ) correctly in both multiplications rather than altering the sequence. He needs to multiply by 10, subtract the original equation, and solve accordingly. This way, he arrives at a more straightforward and accurate method of converting the repeating decimal into a fraction.