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Chapter 2: Problem 2

Convert \(16 \%\) to a decimal

Short Answer

Expert verified
16% as a decimal is 0.16.

Step by step solution

01

Understand what a percentage means

A percentage represents a part per hundred. The symbol % stands for 'per hundred,' so 16% means 16 per 100.
02

Convert Percentage to Fraction

Write the percentage as a fraction by placing the percentage number over 100. For 16%, this would be \( \frac{16}{100} \).
03

Convert Fraction to Decimal

To convert the fraction into a decimal, divide the numerator by the denominator. Calculate \( 16 \div 100 \) which equals 0.16.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Decimal Conversion
Converting percentages to decimals is straightforward once you understand the basic concept. A percentage is essentially a fraction of 100, so to turn it into a decimal, you move the decimal point two places to the left. For example, converting 16% to decimal involves taking the number 16 and adjusting the decimal point: 16.0 becomes 0.16. This technique works every time you need to make such conversions.

Remember this simple rule:
  • Move the decimal point two places left
By mastering this, you can convert any percentage into its decimal form in seconds.
Fractions
Fractions are a way to express parts of a whole number, consisting of a numerator and a denominator. In the context of percentages, the transition from a percentage to a fraction is valuable for converting to a decimal. A percentage like 16% can be expressed as a fraction by writing it over 100, becoming \( \frac{16}{100} \). This establishes a ratio, making further conversions easier.

Tips for understanding fractions include:
  • The numerator (top number) represents the part you have.
  • The denominator (bottom number) shows the total number of equal parts.
  • Fractions represent a part of a single whole.
Using fractions can simplify other mathematics operations, such as when adding, subtracting, or converting them to decimals.
Mathematical Operations
Mathematical operations are key in solving conversion problems like turning percentages into decimals. Once you have a percentage expressed as a fraction, the next step is using division - a primary mathematical operation. Dividing the numerator by the denominator in a fraction like \( \frac{16}{100} \) lets us convert it to a decimal. Performing the division \( 16 \div 100 \) gives us 0.16.

Understanding these operations helps in achieving correct conversions:
  • Addition and subtraction modify numbers, while multiplication and division adjust ratios and scales.
  • Division, in particular, is crucial for transforming fractions to decimals.
Mastering these operations simplifies many math tasks and aids in both everyday applications and academic challenges.

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Most popular questions from this chapter

You leave a tip for \(\$ 7.50\) for a bill at a restaurant that is \(\$ 44.50 .\) What percent tip did you leave?

You deposit \(\$ 1,000\) in an account that earns simple interest. The annual interest rate is \(2.5 \%\). a. How much interest will you earn in 5 years? b. How much will you have in the account in 5 years?

A friend lends you \(\$ 200\) for a week, which you agree to repay with \(5 \%\) one-time interest. How much will you have to repay?

Tom has misplaced the sales contract for his car and cannot remember the amount he originally financed. He does know that the interest rate was \(9.6 \%\) APR for 60 months and the simple interest loan required a total of 60 payments at \(\$ 254.23 .\) What is the amount of money that Tom borrowed?

Consider an investment of \(\$ 20000\) with an annual interest rate of \(5 \%\). a. If that investment is earning simple interest, how much will the investment be worth in 10 years? b. If that investment is getting annually compounding interest, how much will the investment be worth in 10 years?
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