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Chapter 5: Problem 32

In the following exercises, convert each decimal to a fraction or mixed number. $$0.373$$

Short Answer

Expert verified
0.373 = \( \frac{373}{1000} \)

Step by step solution

01

Understand the Decimal

The given decimal is 0.373. This is a proper decimal as it is less than 1.
02

Write as a Fraction

To convert 0.373 to a fraction, consider it as \( \frac{0.373}{1} \). To remove the decimal, multiply both the numerator and the denominator by 1000 (since there are three digits after the decimal point). Therefore: \( 0.373 = \frac{0.373 \times 1000}{1 \times 1000} = \frac{373}{1000} \)
03

Simplify the Fraction

Check if \( \frac{373}{1000} \) can be simplified further. Since 373 is a prime number and not a factor of 1000, \( \frac{373}{1000} \) is already in its simplest form.

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Key Concepts

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

decimal numbers
Decimals are a way to represent fractions or parts of a whole number. They are based on powers of 10. For example, in the decimal number 0.373, the digits 3, 7, and 3 are in the tenths, hundredths, and thousandths places respectively. This means 0.373 is actually \(3\) tenths, \(7\) hundredths, and \(3\) thousandths.
This understanding is crucial for converting decimals into fractions. If you're comfortable with what each place value means, you can easily convert any decimal into a fraction. Let鈥檚 see how this applies to converting 0.373 into a fraction.
fractions
Fractions represent a part of a whole or, in simpler terms, a division of integers. The fraction \[ \frac{a}{b} \] denotes that 'a' is divided by 'b'.
To convert a decimal into a fraction, you need to remember how decimals translate into place values. For instance, the decimal 0.373 means 373 divided by 1000 because 373 is in the thousandths place.
For another example, consider 0.5. This is read as five-tenths, which can be written as \[ \frac{5}{10} \]. Fractions like this one can often be simplified, which we'll go into next.
This simplification step can make the fraction easier to understand and work with.
simplifying fractions
Simplifying fractions means making the fraction as simple as possible. To do this, you find the greatest common divisor (GCD) of the numerator and the denominator, and divide both by that number.
However, in the given solution for 0.373, we found that the fraction \[ \frac{373}{1000} \] cannot be simplified further because 373 is a prime number and not a common factor of 1000.
Let鈥檚 consider a different example for clarity. Take \[ \frac{8}{12} \]. The GCD of 8 and 12 is 4. When you divide both the numerator and the denominator by 4, you get \[ \frac{2}{3} \]. This is the simplified form.
Remember, simplifying makes working with fractions easier, and often more intuitive.

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