Question

Write each percent as a decimal number. $$11.6 \%$$

Short answer

Answer: The decimal representation of 11.6% is 0.116.

Step-by-step solution

Write the percentage as a fraction

To convert the percentage into a decimal, first write the percentage as a fraction over 100: $$\frac{11.6}{100}$$

Convert the fraction to a decimal

Divide the numerator by the denominator to get the decimal value: $$\frac{11.6}{100} = 0.116$$

Write the answer

The decimal representation of 11.6% is 0.116.

Key concepts

Percent to Decimal Conversion

Understanding how to convert a percentage to a decimal is an essential skill in mathematics. This process involves diving the percentage value by 100. Why 100? Because 'percent' literally means 'per hundred', so when you're dealing with percentages, you're working with parts out of 100.

Let's apply this to an example. Say we have 11.6%. To convert this to a decimal, you divide 11.6 by 100, which means you're finding out how much 11.6 is out of one whole unit instead of a hundred. This process gives us the decimal value of 0.116. Now you might wonder why we don’t have additional zeros in front of 0.116. The answer simply comes down to the fact that zeros to the left of the first non-zero digit in a decimal do not contribute any value and therefore are not necessary.

Decimal Representation

The decimal representation of a number is a way to express numbers by using a decimal point to separate the whole number part from the fractional part. It's written to the base 10, which is the standard counting system used in most everyday circumstances.

For example, the decimal representation of the percentage 11.6% as shown in our exercise is 0.116. Decimals are a straightforward way to convey fractions and other real numbers without the use of complex notations. This simplicity is empowering because it makes calculations and comparisons easier and helps us apply these concepts to real-world situations like calculating discounts or interest rates.

Numerical Fraction

A numerical fraction represents a part of a whole. It consists of a numerator, which is the number above the fraction bar, and a denominator, which is the number below it. The process of converting a percent to a decimal, as seen in our example with 11.6%, involves viewing the percentage as a fraction—a numerical fraction with a denominator of 100, since percent means per hundred.

You simplify this fraction by dividing the numerator by the denominator, effectively converting our numerical fraction to a decimal. This is a convenient way to make sense of percentages because it aligns with the base-10 system we use for counting. Just remember that converting a percentage to a numerical fraction simply involves writing the percent value over 100 and then simplifying if necessary.