Understanding Decimals

What Are Decimals? 🔢

A decimal is another way to show parts of a whole. You already know one way to do this: fractions. Decimals are just a different costume for the same idea!

Look at the number $3.45$. That little dot in the middle is called the decimal point. It separates the whole part from the part that is less than one.

• The numbers to the left of the dot are whole ones.
• The numbers to the right of the dot are parts smaller than one whole.

When you see money, you are already reading decimals. A price like $3.45 means 3 whole dollars and 45 cents (a part of a dollar).

Place Value with Decimals

Each digit sits in a place, and that place tells you its value. After the decimal point come the tenths place and the hundredths place.

Let's break down $3.45$:

Ones	.	Tenths	Hundredths
3	.	4	5

• 3 is in the ones place → 3 whole ones.
• 4 is in the tenths place → $\frac{4}{10}$ (4 tenths).
• 5 is in the hundredths place → $\frac{5}{100}$ (5 hundredths).

A tenth means one whole is split into 10 equal parts. A hundredth means one whole is split into 100 equal parts. The farther right you go, the smaller each part becomes.

Reading Decimals Out Loud

When you read a decimal, the decimal point is read as the word "and", and the last digit tells you the place name.

• $0.3$ → "three tenths"
• $0.45$ → "forty-five hundredths"
• $2.7$ → "two and seven tenths"

Worked example: How do we read $0.6$?

• The 6 is in the tenths place.
• So $0.6$ is read as "six tenths", which is the same as $\frac{6}{10}$.

Quick Concept Check ✅

You just learned the names of the places after the decimal point. Let's make sure it stuck!

Worked Example: Naming Each Digit

Let's carefully read the number $5.28$ one place at a time.

Step 1 — Find the whole part. The digit to the left of the decimal point is $5$. That is 5 ones.

Step 2 — Find the tenths. The first digit after the point is $2$. That is 2 tenths, or $\frac{2}{10}$.

Step 3 — Find the hundredths. The next digit is $8$. That is 8 hundredths, or $\frac{8}{100}$.

So $5.28$ is read as "five and twenty-eight hundredths."

Ones	.	Tenths	Hundredths
5	.	2	8

Worked Example: Decimals and Fractions

Decimals and fractions are best friends. Here is how to switch between them:

• $0.1 = \frac{1}{10}$ (one tenth)
• $0.9 = \frac{9}{10}$ (nine tenths)
• $0.03 = \frac{3}{100}$ (three hundredths)

Worked example: Write $0.4$ as a fraction.

• The 4 is in the tenths place.
• So $0.4 = \frac{4}{10}$.

Now use these ideas to fill in the boxes below.

Your Turn: Fill in the Blanks ✍️

Look at the decimal $0.7$.

1. Write the digit that is in the tenths place.
2. Write $0.7$ as a fraction over 10 (type it like $7/10$).
3. In the number $4.6$, write the digit in the ones place.

Guided Practice: Choose the Best Answer 🧠

Read each question carefully and pick the correct choice.

Guided Practice: Match Each Decimal 🔽

Use the place value names you learned. Choose the correct place for each digit.

Decimals in Real Life: Money 💵

You use decimals every single time you spend or save money! In dollars and cents, the decimal point separates whole dollars from cents.

• $0.25 = 25 cents = one quarter
• $0.50 = 50 cents = a half dollar
• $1.75 = 1 dollar and 75 cents

Decimal	In Words	Coins / Value
$0.10	ten cents	one dime
$0.25	twenty-five cents	one quarter
$0.50	fifty cents	two quarters

Because $0.25 $= \frac{25}{100}$, and $\frac{25}{100} = \frac{1}{4}$, a quarter really is one fourth of a dollar. Let's use this in a real problem!

Word Problem: At the Store 🛒

Maya has some coins.

1. She has one quarter. How many cents is that? (Type just the number of cents.)
2. A pencil costs $0.50. How many cents is that?
3. A dime is worth $0.10. How many cents is that?

Word Problem Check ✅

Use what you know about money and decimals.

Review: Everything You Learned 🌟

You now know that decimals are another way to write parts of a whole, just like fractions. Here is a quick summary:

Idea	Example	Same As
Ones place	the 2 in $2.5$	2 whole ones
Tenths place	the 5 in $2.5$	$\frac{5}{10}$
Hundredths place	the 3 in $0.03$	$\frac{3}{100}$
Decimal to fraction	$0.25$	$\frac{25}{100} = \frac{1}{4}$
Money	$0.50	50 cents = a half dollar

Remember: the first place after the decimal point is tenths, and the second place is hundredths. Now try the challenge questions to put it all together!

Challenge Round 🏆

Mix together place value, fractions, and money. You've got this!