Not everything comes in whole numbers — money, heights, and measurements often fall between them. Decimals let us write those in-between amounts using the same place-value idea you already know, just extended past a dot. This lesson shows what the digits after the decimal point mean and how decimals connect to fractions.
You know that places to the left get ten times bigger: ones, tens, hundreds. Decimals extend the same pattern to the right, where each place gets ten times smaller. The decimal point marks where the whole numbers end. The first place after it is tenths (each a tenth of one), then hundredths, and so on.
So 0.3 means 3 tenths, which is the fraction 3/10. The bar below is split into ten equal parts with three shaded — that is 0.3 of the whole bar.
A decimal is really just a fraction with a denominator of 10, 100, 1000… written a shorter way. 0.7 is 7/10. 0.45 is 45/100. Reading two places after the point gives you hundredths, so 0.45 is forty-five hundredths — the same 45-out-of-100 idea as a percentage.
Some decimals equal familiar fractions: 0.5 = 1/2 (five tenths is a half), 0.25 = 1/4, and 0.1 = 1/10. Knowing these by heart helps you move between decimals, fractions and percentages easily.
To compare decimals, line up the decimal points and compare digit by digit from the left, just like whole numbers. A common trap: 0.5 is bigger than 0.45, even though 45 looks like a bigger number than 5 — because 0.5 is five tenths (0.50) while 0.45 is forty-five hundredths, and 50 hundredths is more than 45.
A safe trick is to give them the same number of decimal places by adding zeros: 0.5 becomes 0.50, and now 0.50 versus 0.45 is easy to compare. Money works exactly this way — $0.50 is more than $0.45.
Try these. Pick an answer to see whether it's right and why.