Question

How do you convert $ \dfrac{7}{16} $ into a decimal and percent?

Answer 1

Hint:
Divide 7 by 16 to convert into the required decimal form. Since 7 is smaller than 16, our answer will be of the form 0.abc... (see Note below).
Remember that the "%" sign is read as "per cent" and it stands for "per 100". Recall that 'a' parts out of 'b' equal parts is a value equal to the fraction $ \dfrac{a}{b} $ . A value of x% (x per 100, or x parts out of 100 equal parts) is equal to $ \dfrac{x}{100} $ in fraction. So, our answer must be the value of x, when $ \dfrac{7}{16} $ is expressed in the $ \dfrac{x}{100} $ form, i.e. the denominator must be 100.

Complete Step by step Solution:
In order to convert $ \dfrac{7}{16} $ into decimal easily, let's turn the denominator into a power of 10, by multiplying / dividing both the numerator and the denominator by some appropriate number. Since 2 × 5 = 10, and 16 = 2 × 2 × 2 × 2, the required multiplier is 5 × 5 × 5 × 5.
∴ $ \dfrac{7}{16} $ = $ \dfrac{7}{2\times 2\times 2\times 2} $ × $ \dfrac{5\times 5\times 5\times 5}{5\times 5\times 5\times 5} $
⇒ $ \dfrac{7}{16} $ = $ \dfrac{7\times 5\times 5\times 5\times 5}{10\times 10\times 10\times 10} $
⇒ $ \dfrac{7}{16} $ = $ \dfrac{4375}{10000} $
⇒ $ \dfrac{7}{16} $ = 0.4375
To convert into percentage, we know that we can multiply / divide both the numerator and the denominator of a fraction by the same quantity, without changing its value. In order to get a 100 in the denominator, let's multiply both of them by 100:
⇒ $ \dfrac{7}{16} $ = 0.4375 × $ \dfrac{100}{100} $
This can be written as:
= $ \dfrac{43.75}{100} $ , which means 43.75 percent of 43.75%.

Note:
Percent is abbreviated as "%" which means "per 100" which is just a ratio in which the second number is 100 that is represented in short using the symbol %.
x% is basically equal to $ \dfrac{x}{100} $ in fraction, which can be simplified into its lowest form or can be converted into decimal easily.
Real numbers are of two types:
1) Rational: A rational number is a number which CAN BE expressed in the form $ \dfrac{a}{b} $ , where a and b are integers and $ b\ne 0 $ . Rational numbers are either terminating or non-terminating and repeating in decimal form. e.g. $ \dfrac{17}{5}=3.4 $ , $ \dfrac{52}{9}=5.7777...=5.\bar{7} $ etc.
2) Irrational: An irrational number is a number which CANNOT BE expressed in the form $ \dfrac{a}{b} $ , where a and b are integers. Irrational numbers are non-terminating and non-repeating when expressed in decimal form. e.g. $ \sqrt{2}=1.414213... $ , $ \dfrac{2}{\sqrt{3}+1}=\text{0}\text{.73205}... $ , $ \pi =3.14159... $ etc.