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 89

Textbook Question

Write each decimal as a fraction. (Do not write in lowest terms.) 0.043

Verified step by step guidance

Start by identifying the place value of the last digit in the decimal. In 0.043, the last digit 3 is in the thousandths place.

Write the decimal as a fraction with the decimal number as the numerator and the place value as the denominator. For 0.043, this becomes \( \frac{43}{1000} \).

Ensure that the fraction is not simplified, as the problem specifies not to write in lowest terms.

Verify that the fraction correctly represents the decimal by considering the place value of each digit.

Conclude that \( \frac{43}{1000} \) is the correct representation of the decimal 0.043 as a fraction.

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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 0.043, the '0' is the whole number part, and '043' represents the fractional part. Understanding how decimals work is essential for converting them into fractions.

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, one must express the decimal as a fraction where the decimal digits are placed over a power of ten, depending on the number of decimal places. For instance, 0.043 can be expressed as 43/1000.

Conversion Process

The conversion process from decimal to fraction involves identifying the place value of the last digit in the decimal. For example, in 0.043, the last digit '3' is in the thousandths place, which means the fraction will have a denominator of 1000. This process is crucial for accurately representing decimals as fractions without simplifying them.