Problem 75 - Algebra 1

Question

Write the fraction as a decimal. Round to the nearest hundredth if necessary. $$\frac{3}{4}$$

Step-by-Step Solution

Answer

The decimal equivalent of \( \frac{3}{4} \) is 0.75.

Step 1: Divide the numerator by the denominator

Divide the numerator of the fraction (3) by its denominator (4) using a calculator or long division.

Step 2: Interpret the Result

The result from the division process is the decimal equivalent of the fraction. In this case, when \( \frac{3}{4} \) is calculated, it gives 0.75.

Key Concepts

Division

Understanding division is key to converting fractions into decimals. A fraction like \( \frac{3}{4} \) has two parts: the numerator and the denominator. The numerator is the top part of the fraction (3 in this case), while the denominator is the bottom part (4 in this case). To convert this fraction into a decimal, the first step is to divide the numerator by the denominator. Essentially, you are asking how many times does the denominator "fit into" the numerator. Let's apply this concept. For \( \frac{3}{4} \), you divide 3 by 4, resulting in 0.75. This process means that 3 is 0.75 times 4, giving us our decimal representation.

Rounding Decimals

Rounding decimals helps us to simplify numbers, making them easier to interpret or work with. When rounding to the nearest hundredth, you must focus on the first two decimal places. For instance, in converting \( \frac{3}{4} \) into a decimal, we got 0.75. Here, 0.75 is already rounded to the nearest hundredth because it has exactly two digits after the decimal point. However, if you had a number like 0.756, the number in the third place (6 in this case) determines if the second decimal stays the same (if below 5) or rounds up (if 5 or above). Thus, 0.756 would round to 0.76. Rounding helps present a cleaner, more readable number.

Numerator and Denominator

Numerator and denominator are foundational in understanding fractions and their conversion to decimals. The numerator is the number atop the fraction bar indicating how many parts of the whole are being considered. In \( \frac{3}{4} \), 3 is the numerator. The denominator is below the fraction bar and shows into how many parts the whole is divided. Here, it's 4. These terms are crucial when performing division to convert a fraction into a decimal. You can think of the division as taking the numerator, 3, and dividing it into four equal parts, giving you the decimal, which allows you to understand the fraction's size in a different way. Embracing these concepts makes the transition from fraction to decimal smooth!