← IGCSE Computer Science Paper 1

Denary place values

Each denary column is worth 10 times the column to its right (1, 10, 100, 1000). A number is the sum of each digit times its column value, e.g. 345 = 300 + 40 + 5.

Part of: IGCSE Computer Science 0478 — 1.1 Number Systems — Module 4, ACARA Digital Technologies Years 7–8 — Binary Number Representation — Module 6

Understanding Denary place values in IGCSE Computer Science Paper 1

What it does: A digit in the tens column is multiplied by 10, so 7 in the tens column is worth 70. The columns of denary are powers of 10: 10^0 = 1, 10^1 = 10, 10^2 = 100 and 10^3 = 1000. Each denary column is worth 10 times the column to its right. 1, 2, 4, 8 are binary column values. The 0 is in the tens column. 0 x 10 = 0, so it adds nothing but holds the place of the tens. The 4 is in the hundreds column, so it is worth 400, not 40. Splitting 345 into 300, 40 and 5 shows that the number is the sum of digit x column value.

Common mistakes: The tens column is worth 10, not 100. The digit 4 in the tens column is worth 4 * 10 = 40, so the line should be tens ← 4 * 10. The units column is worth 1. Each column to the left is 10 times the one on its right, so tens = 10, hundreds = 100 and thousands = 1000.

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Learning
Duo
In the denary number 345, what is the value of the digit 4?
40 (it is in the tens column)4 (it is in the units column)
Matches
582 = 500 + 80 + 20
↓
The units digit is 2, not 20. The units column is worth 1, so 2 x 1 = 2. It should be 582 = 500 + 80 + 2.
Applying
Meanings
Term
denary place value
Meaning
Each denary column is worth 10 times the column to its right (1, 10, 100, 1000). A number is the sum of each digit times its column value, e.g. 345 = 300 + 40 + 5.
Practice
1000 100 10 1
Testing
Gaps
Tens =
Check Answer
Spots
2hundreds ← 3 * 100
3tens ← 4 * 100

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Quick Questions

1. In the denary number 345, what is the value of the digit 4?
A. 4 (it is in the units column)
B. 40 (it is in the tens column) ✓
The 4 is in the tens column, so it is worth 4 x 10 = 40.
2. Which list shows the first four denary column values, from right to left?
A. 1, 10, 100, 1000 ✓
B. 1, 2, 4, 8
Each denary column is worth 10 times the column to its right. 1, 2, 4, 8 are binary column values.
3. Which expansion of 345 is correct?
A. 3 + 4 + 5
B. 300 + 40 + 5 ✓
Each digit is multiplied by its column value: 3 x 100 + 4 x 10 + 5 x 1 = 300 + 40 + 5.
4. How is each denary column related to the column on its right?
A. It is worth 10 times as much ✓
B. It is worth 2 times as much
Denary is base 10, so each column is 10 times the one to its right. Doubling is for binary (base 2).
5. In the number 7,206, which column is the digit 7 in?
A. Thousands, so it is worth 7000 ✓
B. Hundreds, so it is worth 700
The columns from the right are units, tens, hundreds, thousands. The 7 is in the fourth column, so it is worth 7000.

Match the Pairs

345 = 300 + 40 + 5 → Expanding a denary number by adding each digit multiplied by its column value
1, 10, 100, 1000 → The first four denary column values: units, tens, hundreds and thousands
In the number 4,solid 7 the digit 7 sits in the tens column, so its value is the digit times 10 → 7 x 10 = 70
Each denary column is a power of the base 10, so the thousands column is 10 cubed → 10 ** 3 = 1000
582 = 500 + 80 + 20 → The units digit is 2, not 20. The units column is worth 1, so 2 x 1 = 2. It should be 582 = 500 + 80 + 2.
Columns: 1, 2, 4, 8 (each x2) → Those are binary column values. Denary columns are worth 10 times the column to the right: 1, 10, 100, 1000.

Key Term

denary place value
Each denary column is worth 10 times the column to its right (1, 10, 100, 1000). A number is the sum of each digit times its column value, e.g. 345 = 300 + 40 + 5.

Fill in the Blanks

1. Units = 1 Tens = 10 Hundreds = 100
Hint: Type the value of the tens column, which is 10 times the units column.
2. 345 = 300 + 40 + 5
Hint: Type the value of the digit 4 in the tens column.
3. Hundreds column = 10^2
Hint: Type the power of 10 that gives the hundreds column value.
4. 5 in hundreds: 5 x 100 = 500
Hint: Type the column value of the hundreds column.
5. 2609 = 2000 + 600 + 0 + 9
Hint: Type the digit in the units column, which is worth 1 each.

Spot the Error

Question 1
A number ← 345
B hundreds ← 3 * 100
C tens ← 4 * 100
D units ← 5 * 1
Line C — The tens column is worth 10, not 100. The digit 4 in the tens column is worth 4 * 10 = 40, so the line should be tens ← 4 * 10.
Question 2
A units = 10
B tens = 10
C hundreds = 100
D thousands = 1000
Line A — The units column is worth 1. Each column to the left is 10 times the one on its right, so tens = 10, hundreds = 100 and thousands = 1000.
Question 3
A Each column is 2x the right
B Units = 1, Tens = 10
C Hundreds = 10 x 10 = 100
Line A — Denary is base 10, so each column is worth 10 times the column to its right, not 2 times. A multiplier of 2 belongs to binary.
Question 4
A 728 has 3 digits
B Digit 7 is in the thousands
C Digit 2 is in the tens
Line B — 728 has only 3 digits, so the 7 is in the third column from the right, the hundreds column. It is not in the thousands column.
Question 5
A 4 thousands = 4 * 1000
B 6 hundreds = 6 * 100
C 0 tens = 0 * 10
D 3 units = 3 * 10
Line D — The units column is worth 1, so the digit 3 is worth 3 * 1 = 3. Multiplying by 10 would wrongly make it 30.

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