Problem 82 - Algebra 1

Question

Write the fraction as a decimal. Round to the nearest hundredth if necessary. $$\frac{5}{11}$$

Step-by-Step Solution

Answer

The decimal representation of the fraction 5/11 rounded to the nearest hundredth is 0.45.

Step 1: Division

Start by dividing the numerator (5) by the denominator (11). This can be done by entering '5 ÷ 11' on a calculator to obtain the decimal.

Step 2: Rounding to nearest hundredth

The result of the division is 0.454545.... Since we want to round to the nearest hundredth (the second decimal place), we consider the third decimal digit. In this case, it's 5 which rounds up the second decimal digit to 5. Therefore, the rounded decimal is 0.45.

Key Concepts

Division of Fractions

To convert a fraction into a decimal, one of the fundamental steps involved is dividing the numerator by the denominator. This process is known as the division of fractions. Let's break it down:

• The **numerator** is the top number in a fraction and represents how many parts we have.
• The **denominator** is the bottom number of a fraction and tells us the total number of equal parts the whole is divided into.

In the problem \( \frac{5}{11} \), the numerator is 5, and the denominator is 11. By using division—meaning, we carefully divide 5 by 11—you find the fraction's equivalent decimal form. This can be practically done using a calculator by performing the operation 5 ÷ 11, which yields a repeating decimal of 0.454545....Fraction division transforms the fractional part into a form we more commonly use in everyday calculations: decimals. Understanding this will bridge the gap from pure math problems to real-world applications.

Rounding Decimal Numbers

Converting a fraction to a decimal may sometimes produce a long string of numbers. This is where rounding becomes useful, especially if we need a simpler approximation. Here’s a quick guide to rounding decimals:

• Find the position to which you want to round. In our example, this is the hundredth place, which is the second digit after the decimal point.
• Look at the next digit to the right (the third decimal place). This digit decides whether to round the second digit down or up.

In the decimal 0.454545, the third digit is a 4, which would usually mean rounding down, but it's part of a repeating sequence that rounds up. This yields a neat rounded decimal: 0.45. Rounding makes decimals easier to understand and use, particularly when precision to many decimal places isn’t necessary. This simplification is especially handy in practical scenarios like currency calculations, measurements, and statistics.

Numerator and Denominator

A deep understanding of numerators and denominators is crucial for converting fractions into other forms, like decimals.

• The **numerator** is the top number in a fraction. It illustrates the number of parts out of the whole that we are focusing on.
• The **denominator** is the bottom number. It defines the number of equal parts the whole is divided into.

When you look at a fraction, consider the numerator as the fragment of the pie you have, while the denominator indicates the entirety of the pie. Understanding these fundamental parts helps not only with fraction division but also strengthens your ability to work with percentages and ratios. Appreciating the roles of the numerator and denominator transforms fractions from abstract numbers into tangible concepts that can be easier to handle in calculations and problem-solving.