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Chapter 1: Problem 44

Write each decimal as a fraction. 0.017

Short Answer

Expert verified
0.017 = \( \frac{17}{1000} \)

Step by step solution

01

- Understand the Decimal

Recognize that the decimal 0.017 represents seventeen thousandths.
02

- Write the Decimal as a Fraction

Since the decimal 0.017 goes to the thousandths place, you can write it as a fraction with 1000 as the denominator: \[0.017 = \frac{17}{1000}\]
03

- Simplify the Fraction (if possible)

Check if the fraction \[\frac{17}{1000}\] can be simplified. In this case, the greatest common divisor (GCD) of 17 and 1000 is 1, so it cannot be simplified further.

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Key Concepts

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

Decimal Representation
Deciphering decimals is a fundamental math concept. When you see a decimal, like 0.017, it simply represents a part of a whole number. Decimals have different place values, such as tenths, hundredths, thousandths, and so on. The digit right after the decimal point represents the tenths place. The second digit is the hundredths place, and the third digit is the thousandths place.
So, for 0.017, the '1' is in the hundredths place and the '7' is in the thousandths place, signifying seventeen thousandths. This understanding is crucial for converting decimals to fractions.
Fractions
Fractions express a part of a whole similar to decimals. The top part of a fraction is called the numerator, indicating the number of parts you have. The bottom part is the denominator, showing the total number of equal parts the whole is divided into.
When converting 0.017 to a fraction, we note that it goes to the thousandths place. Therefore, we use 1000 as the denominator. The decimal without the point, '17', becomes the numerator. Consequently, 0.017 transforms into \(\frac{17}{1000}\). This step of conversion links decimals and fractions, making quantities easier to understand and work with in different math contexts.
Simplifying Fractions
Simplifying fractions is about finding the smallest equivalent fraction. To simplify \(\frac{17}{1000}\), you search for the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both numbers without leaving a remainder.
For \(\frac{17}{1000}\), we find that the GCD is 1 because 17 is a prime number and has no common divisor with 1000 other than 1. Hence, \(\frac{17}{1000}\) is already in its simplest form. Simplifying helps in reducing fractions to their most basic version, making calculations easier and results more readable.

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