Lesson 2.2 — Multi-digit Decimal Operations

Welcome back! Today we're working with decimals, and here's the good news right up front: decimals follow the same rules you already know for whole numbers. There's just a little dot to keep track of.

So what is a decimal really? It's a place-value number. Just like we have a tens place and a ones place, decimals keep going past the dot into the tenths place, the hundredths place, and beyond. The decimal point is simply the marker between the whole part and the part of a whole.

Let's talk about the operations, one at a time.

For adding and subtracting, there's one golden rule: line up the decimal points. Stack the numbers so the dots sit in a single column, then add or subtract just like normal, and bring the point straight down. For example, twelve dollars and fifty cents plus three dollars and seventy-five cents. Line up the points, add, and you get sixteen dollars and twenty-five cents.

For multiplying, ignore the points at first. Multiply like whole numbers. Then count how many decimal places were in both factors together, and give your answer that many. So one point two times zero point three: one place plus one place is two places, giving zero point three six.

And here's a fun surprise. One point two times zero point three got smaller! That's because multiplying by a number less than one shrinks the result.

For dividing by a decimal, slide the point in the divisor until it's a whole number, slide the dividend the same amount, then divide as usual.

Quick recap. Add and subtract: line up the points. Multiply: multiply, then count the places. Divide: make the divisor whole. Same math, just mind the dot!