Decimal Equivalence of Tenths and Hundredths
Decimal Equivalence of Tenths and Hundredths is a Grade 4 math skill that establishes the equivalence 1/10 = 10/100 and its decimal form 0.1 = 0.10. Students learn that any number of tenths can be expressed as 10 times as many hundredths: 3 tenths = 30 hundredths, so 0.3 = 0.30. Covered in Chapter 30: Tenths and Hundredths in Eureka Math Grade 4, this equivalence is essential for comparing decimals, adding tenths to hundredths, and understanding that trailing zeros after the decimal point do not change a number's value.
Key Concepts
A decimal's value does not change when a zero is added to the rightmost decimal place. Any number of tenths is equivalent to ten times that number of hundredths. $$0.T = 0.T0$$.
Common Questions
How are tenths and hundredths related?
1 tenth equals 10 hundredths (1/10 = 10/100). This means any decimal expressed in tenths can be rewritten in hundredths by multiplying by 10. For example, 4 tenths = 40 hundredths, so 0.4 = 0.40.
What does the trailing zero in 0.40 mean?
The trailing zero in 0.40 means zero hundredths — showing that the value is expressed to the hundredths place with nothing extra. It clarifies which place value is being used without changing the value. 0.4 and 0.40 are equivalent.
How do I convert 0.7 to hundredths?
Multiply the tenths digit by 10 to get hundredths: 7 tenths x 10 = 70 hundredths. So 0.7 = 0.70. You are expressing the same value using smaller unit fractions (hundredths instead of tenths).
Why does knowing that 0.3 = 0.30 help with decimal comparison?
When comparing decimals like 0.3 and 0.07, converting 0.3 to 0.30 makes both numbers in hundredths: 30 vs. 7. Comparing 30 and 7 is straightforward. Without conversion, digit-count comparison can mislead students into thinking 0.07 is larger.
How does tenths-hundredths equivalence connect to fraction equivalence?
1/10 = 10/100 is a fraction equivalence relationship — the same type students study for fractions like 1/2 = 2/4. In decimal form, this equivalence appears as 0.1 = 0.10. Both representations show the same principle: multiplying numerator and denominator by 10 preserves value.
What chapter in Eureka Math Grade 4 covers tenths and hundredths equivalence?
Chapter 30: Tenths and Hundredths in Eureka Math Grade 4 develops the equivalence between tenths and hundredths decimals, connecting them to fraction equivalence and to place value on the decimal chart.