How do I rename as a fraction and decimal: 55 5/9%?
55 5/9 = 55.55555
FR67YGHJ
To rename 55 5/9% as a fraction and a decimal, follow these steps:
1. Divide the fractional part (5/9) by 100 to convert it to a decimal.
5/9 ÷ 100 = 5/900 = 0.0555555...
2. Add the whole number (55) to the decimal obtained in the previous step.
55 + 0.0555555... ≈ 55.0555555...
Therefore, 55 5/9% can be renamed as a fraction as 5505/9000 and as a decimal approximately 55.056.
To rename the given percentage as a fraction, you can follow these steps:
1. Convert the percentage to a decimal by dividing it by 100. For example, 55 5/9% becomes 55.555...%.
2. Express the decimal as a fraction. For this, you need to identify the place value of the decimal to determine the denominator. In this case, the decimal extends infinitely, indicating a repeating decimal pattern.
3. To determine the fraction, let x represent the repeating decimal. Multiply x by a power of 10 such that it eliminates the repeating part. In this case, multiplying by 1000 should be sufficient, as it aligns with the repeating pattern of 555.
1000x = 555.555...
4. Subtract the original equation from the new one in order to eliminate the repeating part:
1000x - x = 555.555... - 55.555...
Simplifying the equation gives:
999x = 500
5. Divide both sides of the equation by 999 to solve for x:
x = 500/999
Hence, the fraction equivalent of 55 5/9% is 500/999.
To express the fraction as a decimal, you can divide the numerator (500) by the denominator (999) using long division or a calculator. The resulting decimal approximation is approximately 0.5005 (rounded to four decimal places).