Question

3.5 can be expressed in terms of percentage as
A. $$35\mathrm{\%}$$
B. $$350\mathrm{\%}$$
C. $$3.5\mathrm{\%}$$
D. $$0.35\mathrm{\%}$$

Answer 1

Hint: We use the concept of percentage that if given a number we can convert it into percentage by multiplying the number by 100 and writing the percentage sign along with it. Convert the decimal number into fraction and then multiply with 100.
* Convert a decimal number into fraction by writing the number in numerator (without decimal point) and writing $${10}^n$$ in a denominator where $$n$$ is the number of places where the decimal is placed (counting from right end).
* Percentage is a part of a whole or complete. Percentage is always greater than or equal to 0% and always less than or equal to 100%.

Complete step-by-step solution:
We are given the number as 3.5
We convert the decimal number into fraction.
Since the number of digits after the decimal is equal to 1, then the denominator will be$${10}^1=10$$. Numerator contains the number except the decimal point.
We can write $$3.5={\displaystyle \frac{35}{10}}$$
To convert the number into percentage we multiply the number by 100
$$\Rightarrow$$Percentage $$=\left(3.5\times 100\right)\mathrm{\%}$$
Substitute the value of $$3.5={\displaystyle \frac{35}{10}}$$in the bracket
$$\Rightarrow$$Percentage $$=\left({\displaystyle \frac{35}{10}}\times 100\right)\mathrm{\%}$$
Cancel same terms from numerator and denominator
$$\Rightarrow$$Percentage $$=\left(35\times 10\right)\mathrm{\%}$$
Calculate the product inside the bracket
$$\Rightarrow$$Percentage $$=350\mathrm{\%}$$
$$\therefore$$3.5 can be written as $$350\mathrm{\%}$$

$$\therefore$$Option B is correct.

Note: Students might make the mistake of not converting the fraction into simpler form. Keep in mind always cancel all factors between numerator and denominator, else the percentage will not be within 0 and 100. Also, when converting percentage into fraction, we divide the number given in percentage by 100. Here we obtain $$350\mathrm{\%}$$so students might get confused as it is greater than 100%. Keep in mind after cancelling same factors, $$350\mathrm{\%}={\displaystyle \frac{350}{100}}=3.5\mathrm{\%}$$so, it is less than 100%