Representing Decimals in Equivalent Fraction Forms
This Grade 4 Eureka Math skill teaches students to represent decimal numbers in equivalent fraction forms — as mixed numbers and improper fractions — by relating them to tenths and hundredths. Adding a trailing zero renames a decimal in smaller units without changing its value: 2.4 = 2 and 4/10 = 24/10, and 2.4 = 2.40 = 2 and 40/100 = 240/100. For example, 1.8 = 1 and 8/10 = 18/10, and since 1.8 = 1.80, it also equals 1 and 80/100 = 180/100. This flexibility, taught in Chapter 30 of Eureka Math Grade 4, deepens understanding of decimal-fraction equivalence.
Key Concepts
A decimal number can be expressed in various equivalent forms, such as a mixed number or an improper fraction, by relating it to tenths and hundredths. Adding a trailing zero to a decimal renames it in smaller units without changing its value. $$2.4 = 2 \frac{4}{10} = \frac{24}{10}$$ $$2.4 = 2.40 = 2 \frac{40}{100} = \frac{240}{100}$$.
Common Questions
How do you express 1.8 as a mixed number?
1.8 = 1 and 8/10. The whole number 1 and the fractional part 8/10 represent the decimal.
How do you express 1.8 as an improper fraction?
1.8 = 18/10 (18 tenths). You can verify: 18 divided by 10 = 1.8.
How does adding a trailing zero rename a decimal?
1.8 = 1.80 because adding a zero to the hundredths place does not change the value. 1.80 = 1 and 80/100 = 180/100 in hundredths form.
How do you express 2.4 in multiple fraction forms?
2.4 = 2 and 4/10 (mixed number in tenths) = 24/10 (improper fraction) = 2.40 = 2 and 40/100 = 240/100 (hundredths forms).
Why is it useful to rename decimals in equivalent fraction forms?
It builds flexibility for comparing, adding, and converting between decimals and fractions. Many operations are easier when both numbers share the same denominator.