Question

Write each percent as a decimal number. $$135 \%$$

Short answer

Question: Convert 135% to a decimal number. Answer: 1.35

Step-by-step solution

Identify the given percentage

The given percentage is $$135 \%$$.

Convert the percentage to a decimal

To convert the percentage to a decimal, divide the percentage by 100: $$\frac{135}{100}$$.

Simplify the decimal number

When you divide 135 by 100, you get: $$1.35$$.

State the final answer

So, the decimal representation of $$135 \%$$ is $$1.35$$.

Key concepts

Percent to Decimal Conversion

Understanding how to convert percentages to decimal numbers is a fundamental skill in mathematics and everyday life, as it helps you interpret data and perform calculations with ease. A percentage represents a portion out of 100, which directly correlates to the concept of decimals. To convert a percent to a decimal, the main step involves dividing the percentage value by 100.

For example, if we have 135%, we start the conversion process by writing it as \( \frac{135}{100} \). This mathematical step translates to moving the decimal point two places to the left. Thus, 135% becomes 1.35 in decimal form. Remember, the percentage symbol essentially signifies 'per hundred,' which is why this division by 100 accurately represents the conversion.

Why is this important? This conversion allows us to perform various mathematical operations that are only possible with decimal numbers, such as addition, subtraction, multiplication, and division, within complex calculations in fields like finance, engineering, and statistics.

Simplifying Decimals

Simplifying decimals is a process of reducing a decimal number to its simplest form, making it easier to work with and understand. In our example, after converting 135% to a decimal, we get 1.35. This decimal is already in its simplest form, which means that there are no additional steps necessary to simplify it further. However, situations will arise where the decimal will be lengthier or less straightforward.

A Few Tips for Simplifying Decimals:

• Round long decimals to a certain number of significant figures for ease of use, keeping in mind the context that requires precision.
• Remove any trailing zeros after the decimal point that do not contribute to the value of the number.
• Use mathematical operations such as division or multiplication to convert improper fractions into simplified decimals.

Simplified decimals aid in clear communication of numerical information and in performing calculations more efficiently.

Decimal Representation

Decimal representation refers to the way in which numbers are expressed in the base 10 numbering system (decimals). It's a system that describes fractional numbers using a point, known as the decimal point, to separate the whole number part from the fractional part.

In our initial example, 135% is represented as 1.35 in decimal form. The '1' stands for 100%, the '.3' equates to 30%, and the '.05' is equal to 5%. When combined, they build the whole, manifesting 135% as 1.35 in decimal. Understanding decimal representation is critical for daily tasks such as handling money, measuring ingredients in cooking, or dealing with any operation that requires precision.

Decimals are a concise way to express numbers that are not whole and to perform arithmetic using fractions. Proficiency in using decimal representation is a crucial math skill that underpins much of more advanced mathematics and its applied uses in technology, the sciences, and business.