Writing Decimal Numbers as Fractions
Writing decimal numbers as fractions is a Grade 6 math skill in Saxon Math, Course 1 that converts decimals to fraction form by using place value as the denominator. The number of decimal places determines the denominator: one decimal place means tenths (denominator 10), two places means hundredths (denominator 100), three places means thousandths (denominator 1000). For example, 0.7 = 7/10, 0.45 = 45/100 = 9/20, and 0.125 = 125/1000 = 1/8. Students must always simplify the fraction to lowest terms. This skill is foundational for comparing fractions and decimals, and for converting between forms in applied math problems.
Key Concepts
Property The number of places after the decimal point indicates the denominator (10, 100, 1000, etc.). The digits to the right of the decimal point form the numerator. For a mixed number like 3.75, the whole number is 3 and the fraction is $\frac{75}{100}$.
Examples Write 0.5 as a fraction: $0.5 = \frac{5}{10}$, which reduces to $\frac{1}{2}$. Write 2.25 as a mixed number: $2.25 = 2\frac{25}{100}$, which reduces to $2\frac{1}{4}$. Write 0.125 as a fraction: $0.125 = \frac{125}{1000}$, which reduces to $\frac{1}{8}$.
Explanation Every decimal has a secret fraction identity! To unmask it, just count the number of decimal places. One place means tenths, two places mean hundredths, and so on. Put the decimal digits over that place value denominator, and you've revealed the fraction. Don't forget to simplify it to its final, most awesome form by reducing it!
Common Questions
How do you write a decimal as a fraction?
Write the digits after the decimal as the numerator. Use 10, 100, or 1000 as the denominator based on the number of decimal places (tenths, hundredths, thousandths). Then simplify.
How do you write 0.6 as a fraction?
0.6 has one decimal place (tenths), so write 6/10. Simplify by dividing by 2: 6/10 = 3/5.
How do you write 0.35 as a fraction?
0.35 has two decimal places (hundredths), so write 35/100. Simplify by dividing by 5: 35/100 = 7/20.
How do you write 0.125 as a fraction?
0.125 has three decimal places (thousandths), so write 125/1000. Simplify by dividing by 125: 125/1000 = 1/8.
What is the most important step after writing the fraction?
Always simplify to lowest terms. Find the GCF of the numerator and denominator and divide both by it. An unsimplified fraction like 45/100 should be reduced to 9/20.