Converting Decimals to Fractions
Converting decimals to fractions in Grade 7 uses place value: write the decimal digits as the numerator and the place value of the last digit as the denominator, then reduce. In Saxon Math, Course 2, 0.6 = 6/10 = 3/5, 0.375 = 375/1000 = 3/8, and 7.25 = 7 25/100 = 7¼. For mixed decimals, keep the whole number part separate. This skill reinforces place value understanding and is essential for comparing, ordering, and operating with rational numbers in all future math courses.
Key Concepts
Property To write a decimal number as a fraction, we write the digits after the decimal point as the numerator of the fraction. For the denominator of the fraction, we write the place value of the last digit. Then we reduce.
Examples $0.6 = \frac{6}{10} = \frac{3}{5}$ $0.375 = \frac{375}{1000} = \frac{3}{8}$ $7.25 = 7\frac{25}{100} = 7\frac{1}{4}$.
Explanation Think of a decimal as having a secret fraction identity! The numbers after the dot are the top part (numerator). The bottom part (denominator) comes from the place value of the very last digit. If it’s in the tenths place, use 10. Hundredths place? Use 100! Then, just simplify the fraction to its tidiest form.
Common Questions
How do you convert a decimal to a fraction?
Write the decimal digits (without the decimal point) as the numerator. Use the place value of the last digit as the denominator. Then simplify. For example, 0.6 = 6/10 = 3/5.
What denominator do you use for tenths, hundredths, and thousandths?
Tenths → denominator 10, hundredths → denominator 100, thousandths → denominator 1000. The denominator matches the place value of the rightmost decimal digit.
How do you convert a decimal greater than 1?
Keep the whole number part and convert only the decimal portion to a fraction. For example, 7.25 = 7 + 25/100 = 7¼.
Can you convert 0.375 to a fraction?
Yes: 0.375 = 375/1000. Then find GCF (125) and simplify: 375/1000 = 3/8.
Where is converting decimals to fractions taught in Saxon Math Course 2?
This skill is covered in Saxon Math, Course 2, as part of Grade 7 rational number and place value content.
Why is it important to simplify the fraction after converting?
Simplifying gives the fraction in its most useful, recognizable form. 3/8 is cleaner and easier to work with than 375/1000.
What common mistakes do students make when converting decimals to fractions?
Students often use the wrong denominator (confusing tenths with hundredths), forget to count all decimal digits when setting the numerator, or skip the simplification step.