Decimals to Fractions Study Notes

Understanding Decimals and Fractions

Decimals and fractions are two ways to represent parts of a whole. In 4th grade, we focus on understanding the relationship between them, especially for numbers with one or two decimal places.

Decimals as Parts of a Whole

A decimal number uses a decimal point to separate the whole number part from the fractional part. The digits to the right of the decimal point represent tenths, hundredths, thousandths, and so on.

• The first digit after the decimal point represents tenths (e.g., 0.1 is one tenth).
• The second digit after the decimal point represents hundredths (e.g., 0.01 is one hundredth).

Fractions as Parts of a Whole

A fraction represents a part of a whole, written as a numerator over a denominator. The denominator tells us how many equal parts the whole is divided into, and the numerator tells us how many of those parts we have.

Converting Decimals to Fractions

We can convert decimals to fractions by looking at the place value of the last digit in the decimal.

Converting Tenths to Fractions

If a decimal has one digit after the decimal point, it represents tenths. The denominator of the fraction will be 10.

• Example: 0.3 (three tenths) can be written as the fraction \( \frac{3}{10} \).
• Example: 0.7 (seven tenths) can be written as the fraction \( \frac{7}{10} \).

Converting Hundredths to Fractions

If a decimal has two digits after the decimal point, it represents hundredths. The denominator of the fraction will be 100.

• Example: 0.25 (twenty-five hundredths) can be written as the fraction \( \frac{25}{100} \).
• Example: 0.09 (nine hundredths) can be written as the fraction \( \frac{9}{100} \).

Converting Decimals with Whole Numbers

If a decimal has a whole number part, we include it in our mixed number.

• Example: 1.4 (one and four tenths) can be written as the mixed number \( 1\frac{4}{10} \).
• Example: 2.50 (two and fifty hundredths) can be written as the mixed number \( 2\frac{50}{100} \).

Simplifying Fractions (Introduction)

Sometimes, fractions can be simplified to their lowest terms. While full simplification is a more advanced topic, understanding that fractions can be equivalent is important.

• For example, \( \frac{5}{10} \) is equivalent to \( \frac{1}{2} \).

Decimal	Fraction (Tenths)	Fraction (Hundredths)
0.1	\( \frac{1}{10} \)	-
0.5	\( \frac{5}{10} \)	-
0.01	-	\( \frac{1}{100} \)
0.15	-	\( \frac{15}{100} \)
1.2	\( 1\frac{2}{10} \)	-
3.75	-	\( 3\frac{75}{100} \)

📌 Key Takeaway: The number of digits after the decimal point tells you the denominator of your fraction (10 for one digit, 100 for two digits). 💡 Pro Tip: Think of the decimal point as a separator. The numbers after it form the numerator, and the place value of the last digit gives you the denominator.