The decimal point separates the whole number part from the fractional part. After the decimal point, each column represents a fraction: tenths \(\left(\frac{1}{10}\right)\), hundredths \(\left(\frac{1}{100}\right)\), thousandths \(\left(\frac{1}{1000}\right)\).
Example 1 — What is the value of each digit in 3.047?
Step 1
Set up a place value chart: 3 | . | 0 | 4 | 7 (Units | . | Tenths | Hundredths | Thousandths)
Step 2
3 is in the units column → value = 3
Step 3
0 is in the tenths column → value = \(0 \times \frac{1}{10} = 0\)
Step 4
4 is in the hundredths column → value = \(4 \times \frac{1}{100} = \mathbf{0.04}\)
Step 5
7 is in the thousandths column → value = \(7 \times \frac{1}{1000} = \mathbf{0.007}\)
3.047 = 3 + 0 + 0.04 + 0.007
Example 2 — Write 0.3 + 0.05 + 0.002 as a single decimal
Step 1
0.3 → 3 in the tenths column
Step 2
0.05 → 5 in the hundredths column
Step 3
0.002 → 2 in the thousandths column
Step 4
Combine: \(\mathbf{0.352}\)
Place value columns: … | Tens | Units | . | Tenths (÷10) | Hundredths (÷100) | Thousandths (÷1000) | …
✓ Quick Check 1 — Decimal columns
Question 1 of 10
Reading and Writing Decimal Numbers
Decimal numbers can be written in words. Read the whole number part, say "point", then read each digit individually after the decimal point. Alternatively, name the fractional value (e.g. "forty-two hundredths").
Example 3 — Write "seven and forty-two hundredths" as a decimal
Read digits individually after the point: "three", "zero", "six"
Step 4
Answer: "zero point three zero six"
Two ways to say 0.306: "zero point three zero six" OR "three hundred and six thousandths". Both are correct. In the context of measurement, the second form is more precise.
✓ Quick Check 2 — Reading and writing decimals
Question 1 of 10
Place Value and ×/÷ by 10, 100 and 1000
You met multiplying and dividing by 10, 100 and 1000 in Lessons 2.3 and 2.4. Here's the rule again, framed in terms of place value: when you multiply by 10, digits move ONE place LEFT (the number gets bigger). When you divide by 10, digits move ONE place RIGHT (smaller). The decimal point stays fixed — the DIGITS shift.
Example 5 — A packet of rice weighs 0.25 kg. There are 10 packets in a box. What does the box weigh?
Step 1
Multiply: \(0.25 \times 10\) — move digits 1 place left
Step 2
\(0.25 \times 10 = 2.5\) kg
Step 3
Answer: The box weighs 2.5 kg
Common mistake: People say "move the decimal point". The decimal point NEVER moves — it's always between the units and tenths. It's the DIGITS that shift left or right.
✓ Quick Check 3 — Multiply/divide by 10, 100 and 1000
Question 1 of 10
Practice: Decimal Place Value
Answer each question, then click Check All to see your score.
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Question
Answer
Result
1
What column is the 4 in, in 7.342?
2
Calculate 2.5 × 10
3
Calculate 6.3 ÷ 100
4
What is the value of 8 in 5.083?
5
Write 0.4 + 0.06 + 0.009 as a decimal
6
Calculate 0.034 × 1000
7
Write "five and six hundredths" as a decimal
8
Calculate 4500 ÷ 1000
9
What column is the 7 in, in 12.6479?
10
Calculate 81.2 ÷ 10
⚠ Things to Watch Out For
Trailing zeros change meaning: 0.3 and 0.30 are equal in value, but 0.30 shows greater precision. In a measurement context, these mean different things.
Confusing tenths and hundredths: 0.3 = 3 tenths. 0.03 = 3 hundredths. 0.03 is ten times smaller — the position of the digit matters enormously.
Multiplying by 10: Digits shift LEFT one place (not the decimal point shifts right). The value increases by a factor of 10.
Reading decimals aloud: 3.14 is "three point one four" — NOT "three point fourteen". Each digit after the decimal is read separately.
Zeros after the decimal: 2.0 = 2 and 2.00 = 2 — the trailing zeros don't change the value, but DO indicate the level of precision.