Problem 15 - Prealgebra

Question

Write each number as a fraction or a mixed number. Do not reduce your answers. $$0.00305$$

Step-by-Step Solution

Answer

The decimal 0.00305 as a fraction is \(\frac{305}{100,000}\).

Step 1: Identify the Place Value

Examine the decimal number \(0.00305\). The digit \(5\) is in the ten-thousandths place because there are four digits to the right of the decimal point.

Step 2: Write as a Fraction

Based on the place value, the decimal \(0.00305\) can be written as a fraction with a denominator of 10,000. This gives us \(\frac{305}{100,000}\).

Key Concepts

Decimal Place Value

Understanding the decimal place value is crucial when converting decimals to fractions. Each digit in a decimal number has a specific place value, depending on its position relative to the decimal point. For instance, in the decimal number 0.00305:

• The '3' is in the thousandths place because it is the third digit after the decimal point.
• The '0' after '3' is in the ten-thousandths place.
• The final digit '5' is in the hundred-thousandths place since it is four places to the right of the decimal point.

This means you can interpret 0.00305 as having 305 parts out of 100,000. Recognizing these values allows us to convert the decimal into a fraction later.

Mixed Numbers

Mixed numbers are a combination of whole numbers and fractions. They are usually helpful when dealing with quantities larger than one, but they can also be present when converting decimals that exceed the value of one.
However, in your problem, since 0.00305 is less than 1, the solution directly translates into a fraction without reaching a whole number component. Mixed numbers enter the picture when you deal with numbers like 1.305, where the integer part '1' represents the whole, and the decimal part '305' converts into a fraction like above.
Understanding mixed numbers becomes crucial when you must express decimals that pass the value of one seamlessly, turning the decimal part into a proper fraction while retaining the whole number.

Writing Fractions

After recognizing the decimal place values, the step that follows is writing the number as a fraction. The decimal 0.00305 transformed into the fraction involves writing it as parts of a whole.To do so:

• The entire number after zero is placed as a numerator: 305.
• And it is written over 100,000, representing ten-thousandth parts, as the denominator.

This gives the fraction \( \frac{305}{100,000} \). This fraction structurally conveys the same value as the given decimal. Remember not to reduce the fraction here, as per your exercise directions, making it key to understanding decimal fractions.
Writing fractions helps reinforce your understanding of how precise and small quantities can be represented in a way that outlines their value exactly as a decimal would.