Solved Examples – Place Value
This page presents a wide range of fully worked place value examples, progressing from basic ones and tens through to scientific notation, number bases and significant figures. Study each solution carefully before attempting the practice exercises.
Section A – Basic Place Value
Example A1: Identify place values in 6,248
| Digit | Place | Place Value |
|---|---|---|
| 6 | Thousands | 6,000 |
| 2 | Hundreds | 200 |
| 4 | Tens | 40 |
| 8 | Ones | 8 |
Example A2: Write 50,000 + 3,000 + 70 + 4 in standard form
Example A3: Face value vs place value of 9 in 9,306
Section B – Forms of Numbers
Example B1: Write 7,052 in expanded form (two versions)
Example B2: Write "three million, forty-five thousand and nine" in standard form
Example B3: Write 1,000,302 in word form
Section C – Comparing and Ordering
Example C1: Compare 58,340 and 58,304
Thousands and ten-thousands equal. Hundreds: 3 = 3. Tens: 4 > 0.
Example C2: Arrange in ascending order: 0.6, 0.06, 0.606, 0.66
Tenths: 0 < 6 = 6 = 6. For those with equal tenths, compare hundredths: 0 < 0 < 6. Then thousandths: 6 > 0.
Section D – Rounding
Example D1: Round 6,749 to the nearest thousand
Check hundreds digit: 7 ≥ 5 → round up.
Example D2: Round 3.0849 to 2 decimal places
Check thousandths digit: 4 < 5 → round down.
Section E – Powers of 10 and Scientific Notation
Example E1: Write 0.000056 in scientific notation
Move decimal 5 places right to get 5.6. Exponent = −5.
Example E2: Convert 4.02 × 10⁷ to standard form
Move decimal 7 places right.
Section F – Significant Figures
Example F1: How many sig figs in 0.00580?
Leading zeros: not significant. 5, 8 significant. Trailing zero after decimal: significant. Total = 3.
Example F2: Round 7,645 to 2 sig figs
First 2 sig figs: 7, 6. Next digit is 4 < 5 → round down.
Section G – Number Bases
Example G1: Convert binary 10110 to decimal
Example G2: Convert decimal 45 to binary
45÷2=22 R1, 22÷2=11 R0, 11÷2=5 R1, 5÷2=2 R1, 2÷2=1 R0, 1÷2=0 R1
Example G3: Convert hex 3F to decimal
- Always identify the position of a digit before finding its place value.
- Zeros inside a number are significant and hold places.
- Scientific notation: positive exponent = large number; negative = small number.
- Binary: multiply each bit by its power of 2 and sum. Hex: each digit is worth its face value times 16 to the power of its position.
Summary
These 15 worked examples span the full breadth of place value topics. Work through each one, then cover the solutions and try them yourself. Understanding why each step works, not just following the method, is the key to long-term mathematical confidence.