Write 0.416 as a fraction in its simplest form - OCR - GCSE Maths - Question 18 - 2020 - Paper 6
Question 18
Write 0.416 as a fraction in its simplest form.
You must show full working in support of your answer.
Worked Solution & Example Answer:Write 0.416 as a fraction in its simplest form - OCR - GCSE Maths - Question 18 - 2020 - Paper 6
Step 1
Step 1: Express the Decimal as a Fraction
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Answer
To convert the decimal 0.416 into a fraction, recognize that it can be expressed as:
rac{416}{1000}
This is because there are three decimal places, thus the denominator is 1000.
Step 2
Step 2: Simplify the Fraction
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Answer
Next, we simplify the fraction rac{416}{1000} by finding the greatest common divisor (GCD) of 416 and 1000. The GCD is 16.
Now, divide both the numerator and the denominator by their GCD:
ightarrow 416 ÷ 16 = 26}{1000
ightarrow 1000 ÷ 16 = 62.5}$$
However, since 1000 ÷ 16 is not a whole number, we need to continue factoring down. We actually find GCD correctly simplifies it to:
$$ rac{26}{625}$$.
Step 3
Step 3: Final Answer
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Answer
Thus, 0.416 expressed as a fraction in its simplest form is:
62526.
