Problem 78 - Algebra 1

Question

Write the fraction as a decimal. Round to the nearest hundredth if necessary. $$\frac{7}{25}$$

Step-by-Step Solution

Answer

The decimal equivalent of the fraction \(\frac{7}{25}\) is 0.28.

Step 1: Setup the division

The first step in this process is setting up the division of 7 by 25. To convert a fraction to a decimal, the numerator (top number) is divided by the denominator (bottom number). Thus, this is written as: 7 ÷ 25.

Step 2: Perform the division

Next, perform the division operation. Use a calculator to divide 7 by 25.

Step 3: Round if necessary

From Step 2, when 7 is divided by 25, the result is 0.28. Since there is no condition to round to the nearest hundredth, this decimal is the final answer.

Key Concepts

Division

When we talk about converting fractions to decimals, division plays a crucial role. In essence, the process of changing a fraction into a decimal is about dividing the numerator by the denominator. Let's think of a simple example using the fraction \(\frac{7}{25}\). Here, you start by dividing 7 by 25.

To do this, you can set up the division in a long division format, or use a calculator to get a precise result. The division tells us how many times 25 fits into 7 while considering decimal points. This requires understanding both whole numbers and decimals in division.

• Perform the division: 7 ÷ 25.

You will find that 25 cannot perfectly fit into 7, which is why we need decimals. After performing the division, the quotient will be 0.28. This is how fractions turn into decimals! Practice with different fractions, and you'll begin to see patterns.

Rounding Decimals

Rounding is an essential part of working with decimals, especially when you need to present clean and precise numbers. After you divide the numerator by the denominator and get a decimal, sometimes you may need to round it to make it more understandable or usable. In our specific example of \(\frac{7}{25}\), the division gives us exactly 0.28, so rounding isn’t necessary. This is because it naturally ends at two decimal places, which is already rounded to the nearest hundredth.

Here’s a quick guide on rounding to the nearest hundredth, in case you come across decimals that don’t end so neatly:

• Identify the digit in the hundredths place (second digit to the right of the decimal point).
• Look at the digit in the thousandths place (third digit to the right of the decimal point).
• If the thousandths place is 5 or above, round up the hundredths place by one.
• If it’s 4 or below, keep the hundredths place unchanged.

This is rounding in action, making numbers more manageable and less cumbersome to work with.

Numerator and Denominator

The terms 'numerator' and 'denominator' are fundamental to understanding fractions and how they function. In a fraction, the numerator is the top number, while the denominator is the bottom number. These two numbers have specific roles that help define the value of the fraction itself.

Consider the fraction \(\frac{7}{25}\) again:

• Numerator: It is 7. It indicates the number of parts you have.
• Denominator: It is 25. It tells you the total number of equal parts that make a whole.

In simple terms, the numerator and denominator together help you understand how much of something you have.

They are the backbone of fractions and play a direct role in division when converting to decimals. By dividing the numerator by the denominator, you seamlessly transition from fractions to decimals, bridging these two mathematical worlds.