Converting Between Decimals and Mixed Numbers
Grade 4 Eureka Math students practice converting between decimals and mixed numbers using tenths and hundredths place values. A decimal like 3.4 becomes the mixed number 3 4/10 because the digits after the decimal point form the fraction numerator and the place value determines the denominator. For hundredths, 5.28 becomes 5 28/100. Reversing the process, 7 3/10 becomes 7.3. This bidirectional fluency is essential for ordering, comparing, and operating with rational numbers.
Key Concepts
A decimal number is equivalent to a mixed number where the whole number part is the same, and the decimal part is written as a fraction. The denominator is a power of 10 corresponding to the place value of the last decimal digit. For example, a decimal $W.d 1d 2$ is equivalent to the mixed number $W \frac{d 1d 2}{100}$.
Common Questions
How do you convert a decimal to a mixed number?
Keep the whole number the same. Write the decimal digits as the numerator of a fraction. Use 10 as the denominator for tenths, 100 for hundredths.
How do you convert 5.28 to a mixed number?
5.28 becomes 5 28/100, since 28 hundredths is the decimal portion.
How do you convert a mixed number like 7 3/10 to a decimal?
The whole number 7 stays before the decimal point. The fraction 3/10 means 3 tenths, so write 7.3.
What denominator do you use for tenths vs hundredths?
Tenths use a denominator of 10 (one decimal place). Hundredths use a denominator of 100 (two decimal places).
Why is converting between decimals and mixed numbers important?
It builds flexibility with rational number representations, which is needed for comparing, ordering, and operating on numbers in Grade 4 and beyond.