Problem 23 - Introductory Algebra for College Students

Question

Express each rational number as a decimal. $$\frac{7}{20}$$

Step-by-Step Solution

Answer

The decimal representation of \(\frac{7}{20}\) is 0.35.

Step 1: Identify the Numerator and the Denominator

In the given rational number \(\frac{7}{20}\), 7 is the numerator and 20 is the denominator.

Step 2: Division

Divide the numerator by the denominator. That is, divide 7 by 20.

Step 3: Write the Result as a Decimal

The result of the division from step 2 is 0.35, which is the decimal equivalent of the original fraction.

Key Concepts

Numerator and Denominator

When you look at a fraction like \(\frac{7}{20}\), it has two main parts: the numerator and the denominator. The numerator is the number above the line, and it tells us how many parts we have. In this case, the numerator is 7.

• Represents how many parts there are.

On the bottom, you have the denominator, which is 20 in this fraction.

• Shows how many total equal parts make up a whole.

Understanding these parts is crucial. The fraction \(\frac{7}{20}\) tells us that 7 parts out of 20 are being considered.

Decimal Conversion

Decimal conversion is changing a fraction into a decimal number, which expresses a portion of a whole in tenths, hundredths, etc. The process involves division. By converting fractions to decimals, we can often more easily compare, add, or subtract numbers.

• A decimal shows exactness and is easier for computation.

In solo practice, convert fractions like \(\frac{7}{20}\) directly through division, as this provides a precise decimal form.

Fraction to Decimal

Changing a fraction to a decimal is simple and hinges on division. Take the fraction \(\frac{7}{20}\) for example. Here is how you convert it using division:1. To transform \(\frac{7}{20}\), divide 7 by 20. - This calculation involves considering how many times 20 fits into 7, necessitating further expansion into decimal places.2. Performing this division, you find it goes 0 times, so consider 7.0 then continue: - It becomes evident that 20 goes into 70 three times (60), leaving 10. - Borrow another zero to make it 100, and 20 fits five times here.3. Therefore, divide to yield the decimal 0.35. - This conversion shows that \(\frac{7}{20}\) is equivalent to 0.35. By understanding the division process, you can convert fractions between forms easily. Try practicing with multiple examples to get handy with any fraction transformation.