Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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0:54 minutes

Problem 86

Textbook Question

Write each decimal as a fraction. (Do not write in lowest terms.) 0.82

Verified step by step guidance

Identify the decimal number: 0.82.

Recognize that 0.82 can be expressed as \( \frac{82}{100} \) because the decimal has two digits after the decimal point.

Write the decimal as a fraction with the denominator as a power of 10, where the number of zeros corresponds to the number of decimal places.

The fraction \( \frac{82}{100} \) is the representation of the decimal 0.82.

Note that the problem specifies not to simplify the fraction, so \( \frac{82}{100} \) is the final form.

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Key Concepts

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

Decimal Representation

Decimals are a way of expressing numbers that are not whole, using a decimal point to separate the whole number part from the fractional part. For example, in the decimal 0.82, '0' is the whole number part, and '82' represents the fractional part, indicating 82 hundredths.

Fractions

A fraction represents a part of a whole and is expressed as a ratio of two integers, with a numerator (top number) and a denominator (bottom number). To convert a decimal to a fraction, you can express the decimal as a fraction with a denominator that is a power of ten, based on the number of decimal places.

Conversion Process

To convert a decimal to a fraction, identify the place value of the last digit. For 0.82, the last digit '2' is in the hundredths place, so it can be expressed as 82/100. This process involves writing the decimal as a fraction without simplifying it, as the question specifies not to write in lowest terms.