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Chapter 2: Problem 25

Write the decimal as a fraction. $$0.289$$

Short Answer

Expert verified
The decimal 0.289 as a fraction is written as \(\frac{289}{1000}\).

Step by step solution

01

Identify Decimal Place

Given the decimal number 0.289. The decimal part, 289, is in the thousandths place. Therefore, it can be written as \(\frac{289}{1000}\)
02

Simplification

We identify that the numerator (289) and the denominator (1000) do not have a common divisor other than 1. Hence, this fraction cannot be simplified any further and remains as \(\frac{289}{1000}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Fractions
Fractions represent a part of a whole. When looking at a fraction, it consists of two parts:
  • The numerator: the top number that tells you how many parts are being considered.
  • The denominator: the bottom number that tells you into how many equal parts the whole is divided.
For example, in the fraction \( \frac{1}{4} \), 1 is the numerator and 4 is the denominator, meaning one part out of four equal parts.
Fractions are fundamental in understanding divisions and sharing quantities equally. They can also represent proportions and ratios, giving us insights into relative sizes.
Exploring Decimal Numbers
Decimal numbers are another way to express fractions or parts of a whole. They use a decimal point to separate the whole number part from the fractional part.
The fractional part of a decimal number is based on the powers of ten. For instance, in the number 0.289, the number 289 is in the thousandths place, which means it can be expressed as \( \frac{289}{1000} \).
Decimals are useful because they make arithmetic operations like addition and subtraction straightforward and are easier to compare and order than fractions.
  • A common decimal system is the base-10 system, utilizing digits 0-9.
  • Converting fractions into decimals involves dividing the numerator by the denominator.
Simplification of Fractions
Simplification of fractions refers to reducing the fraction to its smallest form. This involves dividing both the numerator and the denominator by their greatest common divisor (GCD).
A fraction is in its simplest form when no number other than 1 can evenly divide both the numerator and the denominator. This means that both have no common factors.
In some cases, like with \( \frac{289}{1000} \), the fraction is already simplified because 289 and 1000 do not share any common divisors other than 1. Simplifying fractions helps in making them easier to understand and potentially eases comparison between different fractions.
  • Simplifying is sometimes referred to as reducing a fraction.
  • Always check for common factors to simplify correctly.

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