Representing Mixed Numbers with Hundredths
This Grade 4 Eureka Math skill teaches students to decompose mixed numbers with hundredths fractions into their component ones, tenths, and hundredths, and connect this to decimal notation. For example, 1 and 22/100 = 1 + 2/10 + 2/100 = 1.22; and 2 and 35/100 = 2 + 3/10 + 5/100 = 2.35. Special cases like 4 and 8/100 must be handled carefully: 8/100 = 0 tenths + 8 hundredths, giving 4.08. This expanded decimal decomposition skill from Chapter 30 of Eureka Math Grade 4 bridges fraction and decimal representations.
Key Concepts
A mixed number with a fraction in hundredths can be decomposed into ones, tenths, and hundredths. This expanded form directly translates to its decimal representation. $$1 \frac{22}{100} = 1 + \frac{22}{100} = 1 + \frac{2}{10} + \frac{2}{100} = 1.22$$.
Common Questions
How do you convert 2 and 35/100 to a decimal?
Decompose: 2 and 35/100 = 2 + 3/10 + 5/100 = 2.35. The 3 is in the tenths place and the 5 is in the hundredths place.
How do you convert 4 and 8/100 to a decimal?
Since 8/100 has no tenths, the tenths place is 0: 4 + 0/10 + 8/100 = 4.08. The zero placeholder in the tenths place is essential.
How do you convert 1 and 22/100 to a decimal?
1 and 22/100 = 1 + 2/10 + 2/100 = 1.22. The 2 tenths come from the tens digit of 22, and the 2 hundredths from the ones digit.
How do you break a hundredths fraction into tenths and hundredths components?
The tens digit of the numerator gives the tenths, and the ones digit gives the hundredths. For 35/100: 3 tenths + 5 hundredths. For 8/100: 0 tenths + 8 hundredths.
Why is the zero placeholder important in 4.08?
The zero in the tenths place holds the position and shows there are no tenths, only hundredths. Without it, 4.8 would represent a completely different and much larger decimal value.