Decimals Formula

The decimals formula is useful to work with decimals and perform the basic arithmetic operations with decimals. A decimal number consists of an integral whole number and a decimal or a fractional part. These decimals formulas are useful to understand the changing decimal places across the operations.

What are the Decimals Formulas?

The below presented four decimals formulas are helpful to manipulate decimals and perform numerous operations across decimals. Further, with the help of these formulas, we can understand the change of the place value of the decimals across each of the operations.

Formula 1
A fraction with a 10 or a multiple of 10 as its denominator, can be easily expressed in the form of a decimal. Using the decimal formula, the number of decimal places in the answer is equal to the number of zeros in the multiple of 10 in the denominator.

\[ \begin{align} \frac{a}{10} &= 0.a \\ \frac{a}{100} &= 0.0a \\ \frac{a}{1000} &= 0.00a\end{align}\]

Formula 2
A decimal can be converted into a whole number by multiplying it with 10 or a higher power of 10, which is equal to the number of decimal digits.

\[ \begin{align} 0.a \times 10 &= a \\  0.0a \times 100 &=a \\  0.00a \times 1000 &=a\end{align}\]

Formula 3
In the multiplication of decimals, the number of digits (in each of the numbers) after the decimal point is added, and this same number of digits are present after the decimal point in the resultant product.

\[ 0.00a \times 0.0b = 0.0000c\]

Formula 4
In the division of decimals, the difference of decimals in each of the numbers is taken, and this number of decimals is provided in the resultant answer.

\[ \frac{0.000a}{0.0b} = 0.0c\]

Let us try a few examples to better understand the decimal formulas.

Solved Examples on Decimal Formulas

Example 1: Find the product of 0.0012 and 5.628 using decimal formula.

Solution:

\( 0.0012  \times 5.628 = 0.0067536\).

Note: Here in the first number there are four decimals, in the second number there are three decimals, and thus there are a total of seven decimals in the product answer.

Answer: Hence the product is  0.0067536.

Example 2: Find the value of \(0.00576 \div 0.08 \).

Solution:

\( 0.00576 \div 0.08 = \dfrac{0.00576}{0.08} =0.072\).

Note: In the first decimal number in the numerator there are five decimals, in the second decimal number in the denominator there are two decimals, and finally after division the answer has a difference of the number of decimals i.e, three decimals.

Answer: Hence the value is 0.72 using the decimal formula.