Denary place values
Name:
Date:
Class:
A
Quick Questions
Shade in the A or B circle for each question.
1. In the denary number 345, what is the value of the digit 4?
2. Which list shows the first four denary column values, from right to left?
3. Which expansion of 345 is correct?
4. How is each denary column related to the column on its right?
5. In the number 7,206, which column is the digit 7 in?
B
Match the Pairs
Draw a line connecting each item on the left to its match on the right.
| Left column | Right column | |
|---|---|---|
| 1345 = 300 + 40 + 5 | AThe units digit is 2, not 20. The units column is worth 1, so 2 x 1 = 2. It should be 582 = 500 + 80 + 2. | |
| 21, 10, 100, 1000 | B7 x 10 = 70 | |
| 3In the number 4,solid 7 the digit 7 sits in the tens column, so its value is the digit times 10 | C10 ** 3 = 1000 | |
| 4Each denary column is a power of the base 10, so the thousands column is 10 cubed | DExpanding a denary number by adding each digit multiplied by its column value | |
| 5582 = 500 + 80 + 20 | EThe first four denary column values: units, tens, hundreds and thousands | |
| 6Columns: 1, 2, 4, 8 (each x2) | FThose are binary column values. Denary columns are worth 10 times the column to the right: 1, 10, 100, 1000. |
C
Definitions
denary place value
D
Fill in the Blanks
Complete each line of code by filling in the missing parts.
1.
Units = 1
Tens = __
Hundreds = 100
2.
345 = 300 + __ + 5
3.
Hundreds column = 10^_
4.
5 in hundreds: 5 x ___ = 500
5.
2609 = 2000 + 600 + 0 + _
E
Spot the Error
Shade in the letter of the line that contains an error.
Question 1
A
number ← 345
B
hundreds ← 3 * 100
C
tens ← 4 * 100
D
units ← 5 * 1
Question 2
A
units = 10
B
tens = 10
C
hundreds = 100
D
thousands = 1000
Question 3
A
Each column is 2x the right
B
Units = 1, Tens = 10
C
Hundreds = 10 x 10 = 100
Question 4
A
728 has 3 digits
B
Digit 7 is in the thousands
C
Digit 2 is in the tens
Question 5
A
4 thousands = 4 * 1000
B
6 hundreds = 6 * 100
C
0 tens = 0 * 10
D
3 units = 3 * 10
Answer Key
Denary place values
Section A: Quick Questions
Q1
B — 40 (it is in the tens column)
Q2
A — 1, 10, 100, 1000
Q3
B — 300 + 40 + 5
Q4
A — It is worth 10 times as much
Q5
A — Thousands, so it is worth 7000
Section B: Match the Pairs
Q1
345 = 300 + 40 + 5 → Expanding a denary number by adding each digit multiplied by its column value
Q2
1, 10, 100, 1000 → The first four denary column values: units, tens, hundreds and thousands
Q3
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
Q4
Each denary column is a power of the base 10, so the thousands column is 10 cubed → 10 ** 3 = 1000
Q5
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.
Q6
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.
Section C: Definitions
Q1
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.Section D: Fill in the Blanks
Q1
Units = 1
Tens = 10
Hundreds = 100Q2
345 = 300 + 40 + 5Q3
Hundreds column = 10^2Q4
5 in hundreds: 5 x 100 = 500Q5
2609 = 2000 + 600 + 0 + 9Section E: Spot the Error
Q1
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.
Q2
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.
Q3
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.
Q4
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.
Q5
D — The units column is worth 1, so the digit 3 is worth 3 * 1 = 3. Multiplying by 10 would wrongly make it 30.