How do you change a decimal to a fraction when the fraction looks like this 0.4375 or 0.1667? How can I change this to a fraction? I tried dividing it by 100 but it doesn’t give me the right answer.
The Correct Answer and Explanation is:
To convert a decimal to a fraction, you need to follow a few steps to ensure the result is accurate. I’ll explain how to do it for 0.4375 and 0.1667 specifically, as those are the examples you’re working with.
Converting 0.4375 to a Fraction:
- Start by writing the decimal as a fraction:
Write 0.4375 as 437510000\frac{4375}{10000}100004375. This is because 0.4375 has four decimal places, so it is equivalent to 4375 divided by 10,000. - Simplify the fraction:
Now you need to reduce the fraction by dividing both the numerator (4375) and the denominator (10000) by their greatest common divisor (GCD). The GCD of 4375 and 10000 is 125. Divide both 4375 and 10000 by 125: 4375÷12510000÷125=3580\frac{4375 \div 125}{10000 \div 125} = \frac{35}{80}10000÷1254375÷125=8035 - Simplify further:
Now, simplify 3580\frac{35}{80}8035 by dividing both the numerator and denominator by 5: 35÷580÷5=716\frac{35 \div 5}{80 \div 5} = \frac{7}{16}80÷535÷5=167 So, 0.4375 as a fraction is 716\frac{7}{16}167.
Converting 0.1667 to a Fraction:
- Start by writing the decimal as a fraction:
Since 0.1667 has four decimal places, write it as 166710000\frac{1667}{10000}100001667. - Simplify the fraction:
The greatest common divisor (GCD) of 1667 and 10000 is 1, meaning this fraction is already in its simplest form. Therefore, 0.1667 as a fraction is 166710000\frac{1667}{10000}100001667.
General Approach:
- For terminating decimals (decimals that end like 0.4375 or 0.1667), you can follow the method above by writing the decimal over a power of 10 (100, 1000, 10000, etc.) based on the number of decimal places. Then, reduce the fraction by finding the GCD of the numerator and denominator.
- For repeating decimals, the process is slightly different and may involve algebraic methods to express them as fractions.
So, the key takeaway is that dividing by 100 only works if the decimal has two places (like 0.25). For decimals with more places, you divide by 1000, 10000, etc., and then simplify the fraction.
