Place Value

Compare Two Three-Digit Numbers

Compare 463 and 437 by checking each place from left to right. The hundreds digits are equal, so move to the tens: 6 > 3 means 463 > 437.

Example

Compare 463 and 437 from left to right.

highlighted = computed this step

Step 1 — Set up

Line up both numbers by place value.

hundredstensones463437\begin{array}{c|c|c}\text{hundreds}&\text{tens}&\text{ones}\\4&6&3\\4&3&7\end{array}
Compare from highest place value firsttopbottomhundredstensones463437463 ? 437Check hundreds, then tens, then ones only if needed.

Step 2 — Compare hundreds

Compare hundreds: 4 = 4, so check tens.

hundredstensones463437,4=4\begin{array}{c|c|c}\text{hundreds}&\text{tens}&\text{ones}\\\hl{4}&6&3\\\hl{4}&3&7\end{array},\quad 4=4
Hundreds: 4 = 4, so keep goingtopbottomhundredstensones463437463 ? 437The hundreds digits match, so they do not decide.

Step 3 — Compare tens

Compare tens: 6 > 3, so 463 > 437.

hundredstensones463437,6>3,463>437\begin{array}{c|c|c}\text{hundreds}&\text{tens}&\text{ones}\\4&\hl{6}&3\\4&\hl{3}&7\end{array},\quad 6>3,\quad 463>437
Tens: 6 > 3, so 463 > 437topbottomhundredstensones463437first different place463 > 437The tens place is the first different place.

Step 4 — Result

Read the comparison: 463 > 437.

463>437463>437
463 > 437topbottomhundredstensones463437first different place463 > 437The first different place decides; the ones place is not needed here.
digit-comparison To compare two numbers, start at the leftmost (highest) place. The number with the larger digit at that place is greater. Move right only when the digits in the current place are equal.