Is 8/9 Bigger Than 3/10?

Q: Which is bigger: 8/9 or 3/10?

8/9 is bigger. As a decimal, 8/9 = 0.888889 while 3/10 = 0.3.

Q: What is the difference between 8/9 and 3/10?

The difference is 53/90, which equals 0.588889 in decimal form (58.8889 percentage points).

Yes, 8/9 is bigger than 3/10. Hit Compare below to see the visual breakdown and step-by-step solution — or change the fractions to compare your own.

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How to Compare $\frac{8}{9}$ and $\frac{3}{10}$ Step by Step

Wondering how to figure out which fraction is bigger without a calculator? Comparing $\frac{8}{9}$ and $\frac{3}{10}$ is straightforward once you know the right approach. Below we walk through three proven methods for comparing fractions: finding a common denominator, cross multiplication, and converting to decimals. Each method will give you the same answer, so choose the one that feels easiest.

Method 1: Common Denominators

To compare these fractions, we need a common denominator. The denominators are 9 and 10, and the least common denominator (LCD) is 90.

Step 1. Convert $\frac{8}{9}$: multiply numerator and denominator by 10. $\frac{8}{9} = \frac{8 \times 10}{9 \times 10} = \frac{80}{90}$
Step 2. Convert $\frac{3}{10}$: multiply numerator and denominator by 9. $\frac{3}{10} = \frac{3 \times 9}{10 \times 9} = \frac{27}{90}$
Step 3. Compare the numerators: 80 vs 27.
Step 4. Since 80 is greater than 27, we know that $\frac{8}{9} > \frac{3}{10}$.

Method 2: Cross Multiplication

A quicker way to compare fractions is to cross-multiply. Multiply each numerator by the other fraction's denominator:

Step 1. Multiply the numerator of the first fraction by the denominator of the second: $8 \times 10 = 80$.
Step 2. Multiply the numerator of the second fraction by the denominator of the first: $3 \times 9 = 27$.
Step 3. Compare the products: $80 > 27$, so $\frac{8}{9} > \frac{3}{10}$.

Method 3: Decimal Comparison

Convert each fraction to a decimal by dividing the numerator by the denominator:

$\frac{8}{9}$ as a decimal 0.888889

$\frac{3}{10}$ as a decimal 0.3

Difference 0.588889

Since 0.888889 is greater than 0.3, we confirm that $\frac{8}{9} > \frac{3}{10}$. In percentage terms, $\frac{8}{9}$ is 88.8889% and $\frac{3}{10}$ is 30%, a difference of 58.8889 percentage points.

Why Does This Work?

These fractions have different numerators and different denominators, so we can't compare them directly. By converting to a common denominator of 90, we're cutting both quantities into equal-sized pieces. Then 80 pieces vs 27 pieces is a straightforward comparison.

Frequently Asked Questions

Which is bigger: 8/9 or 3/10?

$\frac{8}{9}$ is bigger. As a decimal, $\frac{8}{9}$ = 0.888889 while $\frac{3}{10}$ = 0.3.

What is the difference between 8/9 and 3/10?

The difference is $\frac{53}{90}$, which equals 0.588889 in decimal form (58.8889 percentage points).

How do you compare 8/9 and 3/10?

You can use three methods: find a common denominator and compare numerators, cross-multiply and compare the products, or convert both fractions to decimals. All three methods confirm that $\frac{8}{9}$ $>$ $\frac{3}{10}$.

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