Comparing Decimals

To compare decimals, we must look at the place value of each digit. The first spot to the right of the decimal point is the tenths place. The second spot is the hundredths place. Think of the decimal point as a wall. The closer a digit is to that wall (on the right), the bigger its value! A $7$ in the tenths place ($0.7$) means you have 7 out of 10 equal parts. A $7$ in the hundredths place ($0.07$) means you only have 7 out of 100 equal parts. It is like comparing 7 giant slices of pizza to 7 tiny crumbs!

One of the easiest ways to compare decimals is to think about money. The tenths place represents dimes, and the hundredths place represents pennies. Since it takes 10 dimes to make a dollar, one dime is $0.1$ or $0.10$. Since it takes 100 pennies to make a dollar, one penny is $0.01$. If you are comparing $0.3$ and $0.25$, just think: 'Would I rather have 3 dimes ($30$ cents) or 25 pennies ($25$ cents)?' The dimes win every time!

When we use a 100-grid (a square broken into 100 small boxes), we can see the difference clearly. To model $0.7$, you would color in 7 full columns (70 small squares). To model $0.07$, you would color in only 7 tiny individual squares. The visual area covered by $0.7$ is much larger than $0.07$. This proves that even though they both use the digit 7, their position changes everything.