Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 136

Chapter 1, Problem 136

Complete the table of fraction, decimal and percent equivalents. Fraction in lowest terms(or Whole Number) 1/3 Decimal ? Percent ?

Verified step by step guidance

Step 1: Understand the relationship between fractions, decimals, and percents. A fraction can be converted to a decimal by dividing the numerator by the denominator.

Step 2: Convert the fraction

\frac{1}{3}

to a decimal by performing the division 1 ÷ 3.

Step 3: Express the decimal obtained from the division as a repeating decimal if necessary (for 1/3, the decimal is a repeating 0.333...).

Step 4: Convert the decimal to a percent by multiplying the decimal value by 100. This shifts the decimal point two places to the right.

Step 5: Write the percent value with the percent symbol (%) to complete the table.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Fraction to Decimal Conversion

Converting a fraction to a decimal involves dividing the numerator by the denominator. For example, 1/3 means dividing 1 by 3, which results in a repeating decimal 0.333.... Understanding this process helps in accurately representing fractions as decimals.

Decimal to Percent Conversion

To convert a decimal to a percent, multiply the decimal by 100 and add the percent symbol (%). For instance, 0.333... multiplied by 100 equals 33.3%, which expresses the decimal as a percentage, making it easier to interpret in many contexts.

Simplifying Fractions

Simplifying fractions means reducing them to their lowest terms by dividing numerator and denominator by their greatest common divisor. Although 1/3 is already in lowest terms, this concept ensures fractions are presented in their simplest form for clarity and ease of conversion.

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