How do you convert $87.5\\% $ as a fraction and a decimal? (2024)
Hint: Here we need to know that if we are given the term $n\% $ then it can be denoted in the form of a fraction as $\dfrac{n}{{100}}$ and now we can convert this fraction into the decimal as we know that when we divide any number with ${10^n}$ we only need to shift the decimal from right to left in the numerator before the $n{\text{th}}$ term from the right.
Complete step by step solution: Here we are given the percentage which we need to convert into the fraction and decimal. So let us first convert it into the fraction form. We need to know that when we are given the number with the percent like $n\% $ we can write it as $\dfrac{n}{{100}}$ in the fraction as a percentage is calculated always with respect to $100$ So we can write $87.5\% = \dfrac{{87.5}}{{100}}$ Now we know that in order to remove this decimal we can multiply the denominator with the same power of $10$ as there are a number of digits after the decimal. So we need to multiply here the denominator with $10$ and we will get the decimal removed as: $87.5\% = \dfrac{{87.5}}{{100}} = \dfrac{{875}}{{1000}}$ Now we can know that $875{\text{ and 1000}}$ can be divisible by $25$ as: $ (25)(35) = 875 \\ (25)(40) = 1000 \\ $ So we can cancel it with the common factor and get $\dfrac{{875}}{{1000}} = \dfrac{{35}}{{40}}$ Now here also $35{\text{ and 40}}$ are divisible by their common factor $5$ and we will get: $\dfrac{{35}}{{40}} = \dfrac{7}{8}$ So we get the fraction as $\dfrac{7}{8}$ We know that it is equal to $\dfrac{{875}}{{1000}}$ Now if we compare ${10^n}$ with the denominator that is $1000 = {10^3}$ we will get $n = 3$ Now we need to shift the decimal in the numerator from the position where it is now towards the left $3$ terms. Now we know that in the numerator which is $875$ the decimal point is not there but we can insert it and write it as $875.0$ and now we can move the decimal position three times from right to left. We can write: $875 = 875.0$ Now we will get: $\dfrac{{87.5}}{{100}} = \dfrac{{875.0}}{{100}} = 0.875$
So we can write $87.5\% = 0.875$ in the decimal form.
Note: Here the student must remember that whenever we need to convert fraction with the denominator as ${10^n}$where $n \in Z,n > 0$into a decimal, we just need to shift the decimal in the numerator from right to left till $n$ terms.
a) To convert 77/80 we will divide the numerator by the denominator. On dividing 77 by 80, we get ⇒ 77/80 = 0.9625. b) To convert 12/16 into decimal, we will divide the numerator 12 by the denominator 16. On dividing 12 by 16, we get ⇒ 12/16 = 0.75.
Given numerical value is 87 1/2%. This number can be written as 87.5%. We need to remove the sign "%" by dividing the number by 100. Hence we can conclude that the fraction of the given number is 7/8.
Converting percentages to decimals and fractions is a fundamental math skill. To convert 18% into a decimal, simply divide by 100, resulting in 0.18. To express it as a simplified fraction, find the greatest common factor, which in this case is 2, and divide both the numerator and denominator by it, giving us 9/50.
Ensure the fraction is written with just a numerator and a denominator. (if the number is a mixed number you first need to convert it to an improper fraction).
Divide the numerator by the denominator.
State the answer clearly in the form 'fraction'='decimal'.
To change a percent to a decimal we divide by 100. This is the same as moving the decimal point two places to the left. For example, 15% is equivalent to the decimal 0.15. Notice that dividing by 100 moves the decimal point two places to the left.
How do you Convert Percent to Fraction? To convert a percent to a fraction, we have to remove the percent sign and divide the given number by 100. And, then we express the fractional form of the percentage in the simplest form. For example, 1% is 1/100, 2% is 2/100 which can be reduced to 1/50.
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