Decimal Numbers

Understanding place value beyond the decimal point, comparing decimals, and performing basic operations.

What is a Decimal?

A decimal number has a whole part and a fractional part, separated by a decimal point.

\underbrace{3}_{\text{ones}} . \underbrace{4}_{\text{tenths}} \underbrace{7}_{\text{hundredths}} \underbrace{2}_{\text{thousandths}}

Position	Value
Hundreds	100
Tens	10
Ones	1
Decimal point	—
Tenths	0.1
Hundredths	0.01
Thousandths	0.001

Comparing Decimals

Line up the decimal points. Compare digits from left to right.

Which is greater: 3.47 or 3.5?

$3.47$ vs $3.50$ — tenths: 4 vs 5. Since $5 > 4$ , we get $3.5 > 3.47$ .

Adding and Subtracting

Always line up the decimal points before adding or subtracting.

12.6 + 3.48

  12.60
+  3.48
------
  16.08

Multiplying by Powers of 10

Moving the decimal point:

Multiply by 10 → move point one place right
Divide by 10 → move point one place left

4.35 × 100

Move the point 2 places right: $4.35 \times 100 = 435$

Real world: supermarket shopping bill

A customer buys items costing €3.47, €1.20, and €0.85. The total is $3.47 + 1.20 + 0.85 = 5.52\text{ EUR}$ . Lining up the decimal points ensures that tenths are added to tenths and pence are added to pence — a critical habit at the till.

Real world: engineering tolerances

A manufactured bolt must be $12.50$ mm in diameter with a tolerance of $\pm 0.05$ mm, so any value from $12.45$ mm to $12.55$ mm is acceptable. Engineers compare decimals to the thousandths place to check whether a part passes quality control.

Real world: scientific measurement

A scientist records four temperature readings: $36.6°C$ , $36.85°C$ , $36.7°C$ , and $36.64°C$ . Ordering them from smallest: $36.6, 36.64, 36.7, 36.85°C$ . Comparing decimal precision is essential in laboratories and medical diagnostics.

Tip When comparing decimals, pad shorter decimals with trailing zeros (e.g. 3.4 becomes 3.40) so all numbers have the same number of decimal places before comparing digit by digit.

Practice Problems

Write 0.375 in words and identify the digit in the hundredths position.

Show answer

Three hundred seventy-five thousandths. Hundredths digit: 7.

Calculate: 7.3 − 2.85

Show answer

7.30 − 2.85 = 4.45.

Arrange in ascending order: 0.6, 0.06, 0.606, 0.66

Show answer

0.06, 0.6, 0.606, 0.66.