Decimals

Add Decimals

Add 2.4 + 1.37 by lining up the decimal points, padding 2.4 to 2.40, then adding column by column from right to left: 0+7=7, 4+3=7, 2+1=3, giving 3.77.

Example

Add 2.4 and 1.37 by lining up decimal points.

highlighted = computed this step

Step 1 — Set up

Set up the decimal board.

xxxxxx2.40+1.37x□.□□\begin{array}{rrrrr}\phantom{x}&\phantom{x}&\phantom{x}&\phantom{x}&\phantom{x}\\\phantom{x}&2&.&4&0\\+&1&.&3&7\\\hline\\\phantom{x}&\square&.&\square&\square\end{array}
Line up decimal points: 2.40 + 1.37onestenthshundredthstop240plus137+sum...Write 2.4 as 2.40 so hundredths line up.

Step 2 — Add column

Add column: 0 + 7 = 7, write 7.

xxxxxx2.40+1.37x□.□7\begin{array}{rrrrr}\phantom{x}&\phantom{x}&\phantom{x}&\phantom{x}&\phantom{x}\\\phantom{x}&2&.&4&0\\+&1&.&3&7\\\hline\\\phantom{x}&\square&.&\square&\hl{7}\end{array}
Hundredths: 0 + 7 = 7onestenthshundredthstop240plus137+sum7...Write 7 in the hundredths place; no carry.

Step 3 — Add column

Add column: 4 + 3 = 7, write 7.

xxxxxx2.40+1.37x□.77\begin{array}{rrrrr}\phantom{x}&\phantom{x}&\phantom{x}&\phantom{x}&\phantom{x}\\\phantom{x}&2&.&4&0\\+&1&.&3&7\\\hline\\\phantom{x}&\square&.&\hl{7}&7\end{array}
Tenths: 4 + 3 = 7onestenthshundredthstop240plus137+sum77...Write 7 in the tenths place; no carry.

Step 4 — Add column

Add column: 2 + 1 = 3, write 3.

xxxxxx2.40+1.37x3.77\begin{array}{rrrrr}\phantom{x}&\phantom{x}&\phantom{x}&\phantom{x}&\phantom{x}\\\phantom{x}&2&.&4&0\\+&1&.&3&7\\\hline\\\phantom{x}&\hl{3}&.&7&7\end{array}
Ones: 2 + 1 = 3onestenthshundredthstop240plus137+sum377...Write 3 in the ones place.

Step 5 — Result

Read the result: 3.77.

xxxxxx2.40+1.37x3.77\begin{array}{rrrrr}\phantom{x}&\phantom{x}&\phantom{x}&\phantom{x}&\phantom{x}\\\phantom{x}&2&.&4&0\\+&1&.&3&7\\\hline\\\phantom{x}&3&.&7&7\end{array}
2.40 + 1.37 = 3.77onestenthshundredthstop240plus137+sum377...The decimal point in 3.77 stays under the aligned points.
decimal-addition Line up the decimal points so digits in the same place are in the same column. Pad shorter decimals with trailing zeros if needed. Then add column by column from right to left, carrying as usual. Place the decimal point directly below the decimal points above.