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Chapter 2: Problem 22

Write the decimal as a fraction. $$0.3$$

Short Answer

Expert verified
The decimal \(0.3\) as a fraction is \(\frac{3}{10}\).

Step by step solution

01

Identifying the Decimal Place of 0.3

The given decimal number is \(0.3\). The digit 3 is in the tenths place, meaning the place value of the decimal 0.3 is \(\frac{1}{10}\).
02

Converting the Decimal into a Fraction

Write down the digit of the decimal (without the decimal point) as the numerator over the place value as the denominator. Hence, the decimal \(0.3\) can be written as \(\frac{3}{10}\).

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Key Concepts

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

Decimals
Decimals are numbers that represent parts of a whole. They are written to the right of a decimal point, making them a part of a broader numeric system that allows more precise representations than whole numbers alone.
A decimal number consists of a whole number part and a decimal part separated by a dot called the decimal point.
  • For example, in the number 0.3, '0' is the whole number part, and '3' is the part that tells us how many tenths we have.
  • Decimals are a way to express numbers between integers, allowing us to specify values more accurately.
Fractions
Fractions are another way to represent a part of a whole. While decimals show parts in a base-10 system, fractions show parts using two numbers: a numerator and a denominator, separated by a slash.
Fractions are particularly useful when performing mathematical operations or comparisons between values that may otherwise seem complex.
  • For example, the fraction \(\frac{3}{10}\) represents three parts of a whole divided into ten equal sections.
  • Fractions can be equivalent, meaning they represent the same portion of a whole, such as \(\frac{1}{2}\) and \(\frac{2}{4}\).
Place Value
Place value refers to the value of a digit depending on its position within a number. In the decimal system, each digit to the right of the decimal point is a power of ten. Understanding place value helps in accurately converting decimals to fractions.
The digit 3 in the decimal 0.3 is located in the tenths place.
  • This means the value of the digit 3 is \(3 \times \frac{1}{10}\), which directly converts to the fraction \(\frac{3}{10}\).
  • Further right decimal places become hundredths, thousandths, and so forth. Each step is a division by 10 of the previous place value.
Numerator and Denominator
The numerator and denominator are essential parts of a fraction. The numerator is the top number that represents how many parts we have. The denominator is the bottom number that tells us how many equal parts make up a whole.
To convert a decimal to a fraction, determine these two components.
  • For example, in the fraction \(\frac{3}{10}\), 3 is the numerator indicating the parts of 10 we have.
  • The denominator 10 tells us that the whole is divided into ten equal parts.
  • A strong comprehension of these concepts allows successful conversion from decimals to fractions by correctly placing the parts in the form of a fraction.

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Most popular questions from this chapter

Write the mixed number or whole number as an improper fraction. $$6 \frac{3}{7}$$

Name the place value of the digit 5 . $$432.09157$$

As Give an example of two fractions whose quotient is 1.

Divide and round to the nearest hundredth. Then check by estimating the quotient. $$1.237 \div 0.021$$

Write an equivalent fraction with the given denominator. $$\frac{6}{7}=\frac{}{49}$$
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