Working with Decimals

What Are Decimals? 🔢

A decimal is a way to write numbers that are between whole numbers. The little dot — the decimal point — separates the whole part (on the left) from the part smaller than one (on the right).

You meet decimals every single day:

• Money: a snack costs $2.75
• Sports: a sprinter runs the race in 10.4 seconds
• Cooking: a recipe needs 1.5 cups of sugar

Decimals and fractions are two ways to say the same thing. For example, $0.5$ is the same amount as $\frac{1}{2}$. Both mean "one half."

Place Value: The Secret Code 🗝️

Every digit in a decimal has a place value. As you move right of the decimal point, each place is ten times smaller than the one before it.

Look at the number $3.475$:

So $3.475$ is read as "three and four hundred seventy-five thousandths."

The order is always the same after the point: tenths, then hundredths, then thousandths. Knowing these places is the key to all decimal math.

⭐ The Golden Rule for Adding & Subtracting

When you add or subtract decimals, follow one rule above all others:

Line up the decimal points, one right on top of the other!

When the points are stacked, tenths land under tenths and hundredths land under hundredths. Then you add or subtract just like whole numbers.

  3.45
+ 2.70   ← add a 0 to fill the empty space
------
  6.15

Tip: You can add a 0 to the end of a decimal without changing its value, so $2.7 = 2.70$. This helps keep your columns lined up neatly.

Quick Concept Check ✅

Let's make sure place value makes sense before we move on.

Adding & Subtracting, Step by Step ➕➖

Example 1 — Add: $4.6 + 2.85$

Step 1 — Line up the decimal points (write $4.6$ as $4.60$ to fill the gap):

  4.60
+ 2.85
------
  7.45

Add from right to left: $0+5=5$, then $6+8=14$ (write $4$, carry $1$), then $4+2+1=7$. The answer is $7.45$.

Example 2 — Subtract: $9.3 - 5.74$

  9.30
- 5.74
------
  3.56

Again, line up the points and add a $0$ to make $9.30$. Borrow where needed, and you get $3.56$.

Multiplying Decimals ✖️

When you multiply, you do not need to line up the points. Instead:

1. Multiply as if the numbers were whole numbers.
2. Count the total number of decimal places in both factors.
3. Place the decimal point in the answer so it has that many places.

Example: $2.5 \times 0.3$

• Multiply whole numbers: $25 \times 3 = 75$
• Count decimal places: $2.5$ has 1, and $0.3$ has 1, for a total of 2.
• Put 2 decimal places in the answer: $0.75$

So $2.5 \times 0.3 = 0.75$. ✅

Your Turn ✍️

Solve each problem. Remember to line up the points for adding and subtracting, and count decimal places when multiplying. Type your answers as decimals (like $7.45$).

Mixed Practice 🎯

Work through these two problems carefully.

Choose the Correct Answer 📋

Pick the right value for each problem from the dropdown menus.

Decimals in the Real World 🌎

Decimals show up most often with money and measurement. Word problems just describe a real situation — your job is to find the operation hiding inside.

Watch for clue words:

Example: Maya buys a notebook for $3.45 and a pen for $1.25. How much does she spend in all?

"In all" means add: $3.45 + 1.25 = 4.70$. Maya spends $4.70.

Solve the Word Problems ✍️

Read carefully and type each answer as a decimal (you can drop a trailing zero, so $4.70$ can be typed as $4.7$).

One More Word Problem 🧠

Decimal Skills Summary 🏆

You can now work with decimals four ways. Here is the whole toolkit in one table:

Converting:

• Fraction → decimal: divide the top by the bottom. $\frac{3}{4} = 3 \div 4 = 0.75$
• Decimal → fraction: use place value. $0.75 = \frac{75}{100} = \frac{3}{4}$

Keep these rules close and you can handle any decimal problem. Now try the challenge below!

Mixed Challenge 🚀

These two questions mix everything together. Take your time!