Tenths and Hundredths Equivalence
Tenths and hundredths equivalence is a Grade 4 math skill from Eureka Math where students learn that 1 tenth equals 10 hundredths, allowing them to convert fractions and decimals between these two units. To convert a fraction from tenths to hundredths, multiply both numerator and denominator by 10: 3/10 = 30/100, or equivalently 0.3 = 0.30. This equivalence is the basis for adding fractions with denominators of 10 and 100, such as 3/10 + 5/100 = 30/100 + 5/100 = 35/100. Covered in Chapter 32 of Eureka Math Grade 4, this skill directly prepares students for decimal addition and for understanding that 0.3 and 0.30 represent the same value.
Key Concepts
To convert a fraction from tenths to hundredths, multiply both the numerator and the denominator by 10. This is based on the equivalence that 1 tenth equals 10 hundredths.
$$\frac{x}{10} = \frac{10x}{100}$$.
Common Questions
How many hundredths equal one tenth?
One tenth equals 10 hundredths. This is the core equivalence: 1/10 = 10/100, or in decimal form, 0.1 = 0.10.
How do you convert tenths to hundredths?
Multiply both the numerator and denominator of the tenths fraction by 10. For example, 4/10 becomes 40/100. In decimal form, move from 0.4 to 0.40.
What grade learns tenths and hundredths equivalence?
Tenths and hundredths equivalence is a 4th grade math skill from Chapter 32 of Eureka Math Grade 4, under the Addition with Tenths and Hundredths module.
Why is 0.3 equal to 0.30?
0.3 means 3 tenths and 0.30 means 30 hundredths. Since 3 tenths = 30 hundredths by the equivalence rule, both decimals represent the same value. The extra zero does not add any value.
How does tenths-hundredths equivalence help with decimal addition?
When adding a decimal in tenths to one in hundredths, you first convert the tenths to hundredths so both fractions share a common denominator. Then the numerators can be added directly: 3/10 + 7/100 = 30/100 + 7/100 = 37/100.
What are common mistakes with tenths and hundredths equivalence?
Students sometimes write 3/10 = 3/100 by only changing the denominator without adjusting the numerator. Always multiply both numerator and denominator by the same factor to maintain equivalent value.