Problem 11 - Prealgebra

Question

Write each number as a fraction or a mixed number. Do not reduce your answers. $$9.009$$

Step-by-Step Solution

Answer

The number 9.009 is written as the mixed number \( 9 \frac{9}{1000} \).

Step 1: Identify the Whole Number and Decimal Parts

First, observe the number 9.009. Here, '9' is the whole number part and '.009' is the fractional part of the number.

Step 2: Convert the Whole Number to a Fraction

The whole number '9' can be expressed as a fraction as \( \frac{9}{1} \) since any whole number can be written over 1.

Step 3: Express the Decimal Part as a Fraction

For the decimal '.009', write it as a fraction. Since '009' has three decimal places, it can be expressed as \( \frac{9}{1000} \).

Step 4: Combine Whole Number and Fraction

Now that we have the whole number as a fraction \( \frac{9}{1} \) and the decimal part as \( \frac{9}{1000} \), we combine them to express the original number as a mixed number. The mixed number is \( 9 \frac{9}{1000} \).

Key Concepts

Mixed Numbers

A mixed number is a number that consists of a whole number and a proper fraction combined. This form of number representation helps in visualizing quantities that include both a complete part and a fractional part. For example, when you see \(9 \frac{9}{1000}\), it means that you have 9 whole parts and a little more, specifically \(\frac{9}{1000}\) of one more part. Mixed numbers make it easier to understand and work with values that extend beyond simple integers. It's a handy way to convert decimals into an easy-to-read format, showing exactly how much more you have beyond whole numbers.

Whole Numbers

Whole numbers are the simplest form of numbers that you use every day. They include zero and all positive numbers without any fractional or decimal parts, such as 0, 1, 2, 3, and so on. In the example, the number '9' from 9.009 is a whole number because it doesn’t include any fraction or decimal part initially. When dealing with conversions like decimal to mixed numbers, the whole number stays the same because it doesn’t need additional adjustment aside from being expressed in some contexts as \(\frac{9}{1}\), aiding in combined expressions like mixed numbers.

Fractions

Fractions are numbers that represent a part of a whole. They consist of two parts: a numerator and a denominator. The numerator, located above the division line, shows how many parts you have, while the denominator, below the line, reveals into how many equal parts the whole is divided. For instance, in \(\frac{9}{1000}\), '9' is the numerator, and '1000' is the denominator, indicating that a very small part of one thousand equal parts is taken into consideration. Converting decimals like ".009" to fractions involves identifying the place value of the decimal and re-writing it as a fraction, making complex numbers simpler to visualize and compute with.