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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

Suppose you obtain a \(\$ 3,000\) Certificate of Deposit (CD) with a \(3 \%\) APR, paid quarterly, with maturity in 5 years. a. What is the future value of the CD in 5 years? b. How much interest will you earn? c. What percent of the balance is interest?

Jose' inherits \(\$ 55,000\) and decides to put it in the bank for the next 25 years to save for his retirement. He will earn an average of \(5.6 \%\) APR compounded monthly for the next 25 years. His partner deposits \(\$ 375\) a month in a separate savings plan that earns \(5.6 \%\) APR compounded monthly for the next 25 years. a. How much will each have at the end of 25 years? b. How much interest did each person earn? c. What percent of balance is interest for each person?

You wish to have \(\$ 3,000\) in 2 years to buy a fancy new stereo system. How much should you deposit each quarter into an account paying \(6.5 \%\) APR compounded quarterly?

You deposit \(\$ 10,000\) in an account earning \(4 \%\) APR compounded weekly. a. How much will you have in the account in 25 years? b. How much interest will you earn? c. What percent of the balance is interest? d. What percent of the balance is the principal?

You deposit \(\$ 2,000\) in an account earning \(3 \%\) APR compounded monthly. a. How much will you have in the account in 20 years? b. How much interest will you earn? c. What percent of the balance is interest? d. What percent of the balance is the principal?
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