A Place-Value Transformation

Multiplying by 10, 100, or 1000 scales a number by one, two, or three powers of ten. Each digit moves to a place worth ten times more for every factor of 10. In the previous stage, two-digit subtraction required careful attention to tens and ones. The same place-value awareness now explains why 36 becomes 360 when multiplied by 10: the 3 tens become 3 hundreds, and the 6 ones become 6 tens.

People often learn “add zeros,” but that is only a useful pattern for whole numbers. It does not explain a decimal calculation such as 0.6 × 10 = 6. Thinking about digit value works consistently for whole numbers and decimals.

Where the Skill Appears

Picture ordering 100 packets, with 24 seed labels in each packet. Calculating 24 × 100 = 2,400 gives the total number of labels without repeated addition. Scaling by powers of ten also appears in metric conversions, money stated in tenths or hundredths, and calculations built from friendly multiples.

The skill provides a reasonableness check too. Multiplying a positive number by 100 must make it one hundred times larger. If 3.8 × 100 is reported as 0.038, the digits moved toward smaller values, so the direction is wrong.

Method One: Count the Place Shifts

The place-value shift method uses the number of zeros in the multiplier to count shifts:

Multiplication by 10 means one shift to a place ten times greater.
Multiplication by 100 means two shifts because 100 = 10 × 10.
Multiplication by 1000 means three shifts because 1000 = 10 × 10 × 10.

For 72 × 100, the 7 moves from tens to thousands and the 2 moves from ones to hundreds. The tens and ones places are then empty, so placeholders fill them: 7,200.

For 4.08 × 100, track the digits rather than imagining that the decimal point physically travels. The 4 ones becomes 4 hundreds, the 0 tenths becomes 0 tens, and the 8 hundredths becomes 8 ones. The result is 408.

Method Two: Repeated Scaling

The ten-step ladder applies one multiplication by 10 at a time. This is useful when several decimal places are involved. To evaluate 0.036 × 1000, climb three steps:

0.036 → 0.36 → 3.6 → 36

Each arrow multiplies the current value by 10. The ladder makes it easy to count and provides intermediate checks. It also shows why blindly attaching three zeros to 0.036 would be incorrect.

Four Worked Calculations

58 × 10: Shift the 5 and 8 one place toward greater value. They represent 5 hundreds and 8 tens, so the product is 580.
109 × 100: Apply two ten-steps: 109 → 1,090 → 10,900. The internal zero remains important.
7.25 × 1000: Climb 7.25 → 72.5 → 725 → 7,250. Three shifts produce 7,250.
0.804 × 100: The 8 tenths becomes 8 tens, the zero remains in the ones place, and the 4 thousandths becomes 4 tenths. The answer is 80.4.

Notice that the count of digits after the decimal may shrink, but the important change is the value of every digit. Estimation helps: 0.804 is a little below 1, so one hundred copies should be a little below 100.

Frequent Misunderstandings

Attaching zeros to a decimal: 2.7 × 100 is 270, not 2.700; the latter still has value 2.7.
Moving in the division direction: Multiplication by a power of ten makes a positive number larger, unless the number is zero.
Ignoring zeros inside a number: In 3.06 × 100, the zero preserves the tens-free relationship, producing 306.
Counting multiplier digits instead of zeros: Multiplying by 1000 requires three shifts, not four.
Changing each digit separately by multiplication: Do not turn 23 × 10 into “2 × 10 and 3 × 10” written side by side. Shift their places as one number.

Practice Ideas for This Stage

Create a three-column ladder labelled ×10, ×100, and ×1000, then send one starting number across it. Alternate whole numbers with values below 1 so the place-value rule—not a zero shortcut—does the work. Read answers aloud with units where possible: “0.45 metres times 100 is 45 metres.” Finally, reverse-check with division by the same power of ten. Work slowly enough to count every shift.

Scale These Mentally

34 × 10
81 × 100
6 × 1000
2.9 × 10
0.63 × 100
14.7 × 1000
205 × 10
0.052 × 1000
9.08 × 100
430 × 100
0.9 × 1000
76.4 × 10
1.025 × 1000
0.307 × 100
92 × 1000
5.55 × 100
0.004 × 1000
601 × 10

Sample Mental Ladders

2.9 × 10: One step gives 2.9 → 29.
0.63 × 100: Two steps give 0.63 → 6.3 → 63.
14.7 × 1000: Follow 14.7 → 147 → 1,470 → 14,700.
0.052 × 1000: Climb 0.052 → 0.52 → 5.2 → 52.
0.307 × 100: Use two stages: 0.307 → 3.07 → 30.7.

Completed Products

340; 2. 8,100; 3. 6,000; 4. 29; 5. 63; 6. 14,700; 7. 2,050; 8. 52; 9. 908; 10. 43,000; 11. 900; 12. 764; 13. 1,025; 14. 30.7; 15. 92,000; 16. 555; 17. 4; 18. 6,010.

Stage Questions

Why does a placeholder zero appear?

After digits shift, some lower-value places may be empty. A zero marks each empty place so that the other digits keep their correct values.

Does this work with negative numbers?

Yes. Scale the magnitude by the same place-value rule and keep the negative sign. For example, -4.2 × 10 = -42.

How do I know whether my decimal answer is sensible?

Compare its size with the starting value. Multiplication by 10, 100, or 1000 should increase the magnitude by exactly that factor; a quick estimate reveals most direction errors.

Practice Examples

Example 1: 47 × 10 = ?

Multiplication by 10 makes every digit worth ten times as much
The 4 tens become 4 hundreds, and the 7 ones become 7 tens
A zero holds the empty ones place, giving 470

Answer: 470

Example 2: 36 × 100 = ?

Recognise 100 as 10 × 10, so two place-value shifts are needed
After the first shift, 36 becomes 360
After the second shift, 360 becomes 3,600

Answer: 3,600

Example 3: 5.2 × 1000 = ?

Multiplying by 1000 shifts each digit three places toward greater value
Track three shifts: 5.2 → 52 → 520 → 5,200
Use placeholder zeros where no other digits occupy the places

Answer: 5,200

Example 4: 0.47 × 100 = ?

Shift every digit two places toward greater place value
The 4 tenths becomes 4 tens, and the 7 hundredths becomes 7 ones
Therefore 0.47 × 100 = 47

Answer: 47

Multiplying by 10, 100, and 1000