Question

How do you simplify $0.5 \div 0.001$?

Answer 1

Hint: In this question, we have to simplify $0.5 \div 0.001$. To simplify means to find the value of the given expression. Here, one decimal number has to be divided by another decimal number. So, we first convert both decimal numbers into fractions and then, we divide the first fraction by the second fraction.

Complete step-by-step solution:
We have the first decimal number as $0.5$ and the second decimal number as $0.001$.
We first convert $0.5$ into its fractional form. For this, the decimal number is written in the numerator and the denominator is $1$.
$0.5 = \dfrac{{0.5}}{1}$
Now, we multiply both the numerator and the denominator by $10$.
$\dfrac{{0.5}}{1} = \dfrac{{0.5}}{1} \times \dfrac{{10}}{{10}} = \dfrac{5}{{10}}$
Now we simplify the fraction as
$\dfrac{5}{{10}} = \dfrac{1}{2}$ .
So, $\dfrac{1}{2}$ is the fractional form of $0.5$
Now, we convert $0.001$ into fractions. For this, the decimal number is written in the numerator and the denominator is $1$.
$0.001 = \dfrac{{0.001}}{1}$
Now, we multiply both the numerator and the denominator by $1000$.
$\dfrac{{0.001}}{1} = \dfrac{{0.001}}{1} \times \dfrac{{1000}}{{1000}} = \dfrac{1}{{1000}}$
So, $\dfrac{1}{{1000}}$ is the fractional form of $0.001$.
So, we can write $0.5 \div 0.001$as:
$
  0.5 \div 0.001 \\
   = \dfrac{1}{2} \div \dfrac{1}{{1000}} \\
$
Here, we convert the division sign into the multiplication sign. When we convert division sign into multiplication sign, the fraction after the division sign gets reciprocated.
$
   = \dfrac{1}{2} \times \dfrac{{1000}}{1} \\
   = \dfrac{{1000}}{2} \\
   = 500 \\
$
Hence, $0.5 \div 0.001 = 500$

Note: When we convert the division sign into the multiplication sign, the fraction written after the division sign is not written as it is, but it gets reciprocated. Reciprocated means that the denominator of the fraction becomes the numerator and the numerator becomes the denominator.

Also, while converting a decimal number into a fraction, we calculate the number of digits after the decimal point and we multiply the numerator and the denominator with \[1\] with that many zeros in it. For example, for the decimal number $0.85$to be converted into a fraction, the numerator $0.85$ and the denominator $1$ will be multiplied with $100$.