To compare decimals, use the place value from writing decimals. It works just like comparing whole numbers: start at the greatest place.
Idea clave
Compare the whole numbers first, then the tenths, then the hundredths. It helps to write both decimals with two places: $0.3 = 0.30$. Now $0.30$ and $0.25$ are 30 hundredths and 25 hundredths, so $0.3 > 0.25$.
Por qué funciona
A 0 at the end of a decimal adds 0 hundredths, so it does not change the amount: 3 tenths is exactly 30 hundredths. Writing both with hundredths makes the pieces the same size, and then you can compare like whole numbers. Both decimals must refer to the same whole.
Ejemplo resuelto: Different lengths
Compare $0.3$ and $0.25$.
- Tenths first: 3 tenths and 2 tenths. $3 > 2$.
- Or with hundredths: $0.30$ and $0.25$, and $30 > 25$.
Respuesta: $0.3 > 0.25$
Ejemplo resuelto: With wholes
Compare $1.2$ and $1.19$.
- The wholes match: 1 and 1.
- Tenths: 2 and 1. Since $2 > 1$, stop.
Respuesta: $1.2 > 1.19$
Error común
Thinking the decimal with more digits is larger, so $0.25 > 0.3$ "because 25 > 3." The digits after the point are tenths and hundredths, not whole numbers. Line up the decimal points, or add a zero so both have hundredths.