Tenths and Hundredths

For Elementary Students

What are Decimals?

Decimals are another way to show parts of a whole, just like fractions!

Think about it like this: Money uses decimals — $2.50 means 2 dollars and 50 cents (50 parts out of 100).

The Decimal Point

The decimal point (.) separates whole numbers from parts.

Example: 3.7

• 3 is the whole number (ones place)
• . is the decimal point
• 7 is the part (tenths place)

Tenths Place

The first digit after the decimal point is the tenths place.

Example: 0.4 (zero point four)

This means 4 tenths or 4 out of 10 equal parts.

As a fraction: 0.4 = 4/10

Visual: Imagine a square divided into 10 equal strips. Shade 4 of them.

██ ░░ ░░ ░░ ░░ ░░ ░░ ░░ ░░ ░░
██ ░░ ░░ ░░ ░░ ░░ ░░ ░░ ░░ ░░
██ ░░ ░░ ░░ ░░ ░░ ░░ ░░ ░░ ░░
██ ░░ ░░ ░░ ░░ ░░ ░░ ░░ ░░ ░░

4 out of 10 shaded = 0.4

Reading Tenths

Example: 2.3 = "two and three tenths" = 2 + 3/10

Hundredths Place

The second digit after the decimal point is the hundredths place.

Example: 0.25 (zero point two five)

This means 25 hundredths or 25 out of 100 equal parts.

As a fraction: 0.25 = 25/100 = 1/4

Visual: Imagine a 10×10 grid (100 tiny squares). Shade 25 of them.

██ ██ ██ ██ ██ ░░ ░░ ░░ ░░ ░░
██ ██ ██ ██ ██ ░░ ░░ ░░ ░░ ░░
██ ██ ██ ██ ██ ░░ ░░ ░░ ░░ ░░
(and so on... 25 squares shaded)

25 out of 100 = 0.25

Reading Hundredths

Money and Decimals

Money is the most common use of hundredths!

$1.00 = 100 cents

• Dimes are tenths: 1 dime = $0.10 = 10/100
• Pennies are hundredths: 1 penny = $0.01 = 1/100

Example: $3.47

• 3 dollars (whole)
• 4 dimes (4 tenths = 40 cents)
• 7 pennies (7 hundredths = 7 cents)

For Junior High Students

Place Value Chart

Understanding where each digit sits:

Example: 12.34

• 1 is in the tens place (10)
• 2 is in the ones place (2)
• 3 is in the tenths place (0.3)
• 4 is in the hundredths place (0.04)

Value: 10 + 2 + 0.3 + 0.04 = 12.34

Expanded Form with Decimals

Example: 5.68

5 + 0.6 + 0.08

or

5 + 6/10 + 8/100

Example: 20.15

20 + 0.1 + 0.05

or

20 + 1/10 + 5/100

Converting Fractions to Decimals

Tenths:

• 3/10 = 0.3
• 7/10 = 0.7
• 9/10 = 0.9

Hundredths:

• 12/100 = 0.12
• 45/100 = 0.45
• 99/100 = 0.99

Common fractions:

• 1/2 = 50/100 = 0.50 = 0.5
• 1/4 = 25/100 = 0.25
• 3/4 = 75/100 = 0.75

Zeros in Decimals

Trailing zeros (after the last digit) don't change the value:

• 0.5 = 0.50 = 0.500 (all equal!)
• 2.3 = 2.30 = 2.300

Leading zeros (before the first non-zero digit) don't count:

• 0.07 = "seven hundredths" (the zero in tenths place is just a placeholder)

Comparing Decimals

Example: Which is larger: 0.4 or 0.37?

Line up the decimal points and compare place by place:

0.40  (write 0.4 as 0.40)
0.37

Compare tenths: 4 > 3

Answer: 0.4 > 0.37

(4 tenths is more than 3 tenths, even though 37 looks bigger than 4!)

Decimals on a Number Line

Tenths:

0 ─ 0.1 ─ 0.2 ─ 0.3 ─ 0.4 ─ 0.5 ─ 0.6 ─ 0.7 ─ 0.8 ─ 0.9 ─ 1.0

Hundredths (zooming in between 0.2 and 0.3):

0.20 ─ 0.21 ─ 0.22 ─ 0.23 ─ 0.24 ─ 0.25 ─ ... ─ 0.29 ─ 0.30

Real-Life Uses

Money: $4.75 (4 dollars, 75 cents)

Measurements:

• 3.5 meters
• 12.8 kilograms
• 98.6°F (body temperature)

Sports:

• Race times: 10.25 seconds
• Scores: 9.8 out of 10

Gas prices: $3.89 per gallon

The Pattern Continues

The place value pattern keeps going to the right:

• Tenths: 1/10 = 0.1
• Hundredths: 1/100 = 0.01
• Thousandths: 1/1000 = 0.001
• Ten-thousandths: 1/10,000 = 0.0001

We will learn more about thousandths and beyond later.

Practice