Decimal Place Value Challenge: Finding the Greater Number

Firstly, let's convert the decimal numbers into simple fractions and compare them:

0.33 is divided by 100 because there are two digits after the decimal point, therefore:

$0.33=\frac{33}{100}$

0.34 is divided by 100 because there are two digits after the decimal point, therefore:

$0.34=\frac{34}{100}$

Then we can compare the numbers in the numerator:

\frac{34}{100}>\frac{33}{100}

Therefore, the larger number is 0.34.