Relating Tenths and Hundredths Using Decimals
Relating Tenths and Hundredths Using Decimals is a Grade 4 math skill from Pengi Math that shows the direct mathematical relationship between fractions with denominator 10 and equivalent fractions with denominator 100. Any fraction n/10 can be written as n0/100 by multiplying numerator and denominator by 10, and the decimal 0.n becomes 0.n0. This equivalence bridges the tenths and hundredths place values and is foundational for comparing and adding decimals with different numbers of decimal places in 4th and 5th grade math.
Key Concepts
Property A fraction with a denominator of 10 can be represented as a decimal in the tenths place. For example, $\frac{n}{10}$ can be written as 0.n. By adding a zero to the hundredths place, the tenths decimal becomes a hundredths decimal, 0.n0. This hundredths decimal can then be expressed as a fraction with denominator 100, $\frac{n0}{100}$. Therefore: $$\frac{n}{10} = \frac{n0}{100}$$.
Examples $\frac{3}{10}$ can be written as 0.3. Adding a zero in the hundredths place gives 0.30, which can be written as $\frac{30}{100}$. Therefore, $\frac{3}{10} = \frac{30}{100}$. $\frac{7}{10}$ can be written as 0.7. Adding a zero in the hundredths place gives 0.70, which can be written as $\frac{70}{100}$. Therefore, $\frac{7}{10} = \frac{70}{100}$. $\frac{5}{10}$ can be written as 0.5. Adding a zero in the hundredths place gives 0.50, which can be written as $\frac{50}{100}$. Therefore, $\frac{5}{10} = \frac{50}{100}$. $\frac{8}{10}$ can be written as 0.8. Adding a zero in the hundredths place gives 0.80, which can be written as $\frac{80}{100}$. Therefore, $\frac{8}{10} = \frac{80}{100}$.
Explanation This skill shows how tenths and hundredths are related. A fraction like $\frac{3}{10}$ represents three tenths. By thinking of this as the decimal $0.3$, we can add a zero to the end without changing its value, making it $0.30$. This new decimal represents thirty hundredths, which is written as the fraction $\frac{30}{100}$. Understanding this equivalence is the first step to adding fractions with tenths and hundredths.
Common Questions
How are tenths and hundredths related?
Every tenths fraction can be converted to an equivalent hundredths fraction by multiplying numerator and denominator by 10. For example, 3/10 = 30/100. In decimal form, 0.3 = 0.30. The hundredths representation just expresses the same amount in smaller pieces.
How do you convert a fraction with denominator 10 to denominator 100?
Multiply both numerator and denominator by 10. For example, 7/10 = (7 × 10)/(10 × 10) = 70/100. In decimal form, 0.7 becomes 0.70. The value is unchanged — you multiplied by 10/10, which equals 1.
Why is it useful to express tenths as hundredths?
Expressing tenths as hundredths lets you compare and add decimals with different numbers of decimal places on equal terms. To compare 0.3 and 0.35, rewrite 0.3 as 0.30, then compare 0.30 and 0.35 — now it's clear that 0.35 is greater.
What does n/10 = n0/100 mean?
This formula shows that any fraction with denominator 10 equals a fraction with denominator 100 where the numerator has a 0 added at the end. For example, 4/10 = 40/100, and 9/10 = 90/100. They represent the same value.
When do 4th graders learn about relating tenths and hundredths?
The relationship between tenths and hundredths is covered in 4th grade math. Pengi Math Grade 4 uses this concept to connect fraction and decimal representations and build fluency with decimal place value.
How does relating tenths and hundredths help with adding decimals?
When adding decimals with different numbers of decimal places, you need them in the same place value. For example, to add 0.3 + 0.45, rewrite 0.3 as 0.30 so both are in hundredths, then add: 0.30 + 0.45 = 0.75.
Which textbook covers relating tenths and hundredths for 4th grade?
Pengi Math Grade 4 covers the relationship between tenths and hundredths as part of the decimal and fractions unit, connecting place value understanding to decimal comparison and computation.