Introduction to Decimals

Decimals are a way of representing fractions using a point called the decimal point. They allow us to express values that are not whole numbers. In this lesson, we will explore the basic concepts of decimals, how to read them, and how to convert between fractions and decimals.

What is a Decimal?

A decimal is a fraction whose denominator is a power of 10. For example, the decimal 0.75 can be expressed as the fraction $\frac{75}{100}$ or simplified to $\frac{3}{4}$.

Reading Decimals

When reading decimals, each digit represents a different place value:

• The digit before the decimal point represents whole numbers.
• The first digit after the decimal point represents tenths.
• The second digit after the decimal point represents hundredths, and so on.

For example, in the decimal 3.142:

• 3 is in the units place,
• 1 is in the tenths place,
• 4 is in the hundredths place,
• 2 is in the thousandths place.

Converting fractions to Decimals

To convert a fraction to a decimal, divide the numerator by the denominator. For example, to convert $\frac{1}{4}$ to a decimal:

$$\frac{1}{4} = 1 \div 4 = 0.25$$

Key Questions

• What is the value of the digit in the tenths place of the decimal 4.56?
• How do you convert the fraction $\frac{2}{5}$ into a decimal?
• What is the decimal representation of $\frac{3}{10}$?

Practice Problems

1. Convert $\frac{7}{10}$ to a decimal.
2. Write the decimal 0.9 as a fraction.
3. What is 5.67 rounded to the nearest whole number?

Conclusion

Decimals are an essential part of mathematics that help us work with parts of a whole. Understanding how to read and convert them is a fundamental skill.