When you multiply by a power of 10, every digit shifts left by the number of zeros. Empty column gaps are filled with zeros.
Operation
Effect on digits
Example
Answer
× 10
Move 1 place left
\(56 \times 10\)
560
× 100
Move 2 places left
\(56 \times 100\)
5,600
× 1000
Move 3 places left
\(56 \times 1000\)
56,000
Example 1: Calculate \(308 \times 100\)
Count zeros in 100
100 has 2 zeros, so every digit moves 2 places left.
Apply
\(308 \rightarrow 30{,}800\)
Answer: 30,800
Example 2: Calculate \(26 \times 1000\)
Count zeros in 1000
1000 has 3 zeros → move 3 places left.
Apply
\(26 \rightarrow 26{,}000\)
Answer: 26,000
Example 3: A factory makes 365 items per day. How many in 1000 days?
Set up
\(365 \times 1000\)
Move 3 places left
\(365 \rightarrow 365{,}000\)
Answer: 365,000 items
Example 4: A pallet holds 1,000 bricks. How many bricks are on 47 pallets?
Set up
\(47 \times 1000\)
Move 3 places left
\(47 \rightarrow 47{,}000\)
Answer: 47,000 bricks
💡 Shortcut for whole numbers: counting the zeros in the multiplier tells you how many zeros to write at the end. \(34 \times 100\) — two zeros in 100, so write "3400". This is the result of digits shifting left, not a rule for decimals.
The same rule applies: all digits shift left by the number of zeros. The decimal point stays fixed — it is the digits that move. This often means the decimal point appears to move right.
⚠️ Never say "add a zero" — it only works for whole numbers. \(0.4 \times 10 = 4\), not 0.40. Always think: digits move left (or equivalently: the decimal point moves right).
Number
× 10
× 100
× 1000
0.7
7
70
700
0.45
4.5
45
450
2.8
28
280
2,800
0.036
0.36
3.6
36
Example 1: Calculate \(0.4 \times 10\)
Shift digits 1 place left
\(0.4\) has a 4 in the tenths column. Moving it 1 place left puts it in the units column.
Result
\(0.4 \rightarrow 4\)
Answer: 4
Example 2: Calculate \(0.07 \times 100\)
Shift digits 2 places left
\(0.07\) — the 7 is in the hundredths column. Moving 2 places left puts it in the units column.
Result
\(0.07 \rightarrow 7\)
Answer: 7
Example 3: Calculate \(2.45 \times 100\)
Shift digits 2 places left
The 2 moves from units to hundreds, the 4 from tenths to tens, the 5 from hundredths to units.
Result
\(2.45 \rightarrow 245\)
Answer: 245
Example 4: Calculate \(0.063 \times 1000\)
Shift digits 3 places left
0 → thousands (stays 0), 0 → hundreds (stays 0), 6 from hundredths → tens, 3 from thousandths → units.
Result
\(0.063 \rightarrow 63\)
Answer: 63
Example 5: A recipe needs 0.35 kg of flour for 1 portion. How much for 100 portions?
Set up
\(0.35 \times 100\)
Shift 2 places left
\(0.35 \rightarrow 35\)
Answer: 35 kg
💡 Unit conversion shortcut: km → m multiply by 1000 | m → cm multiply by 100 | cm → mm multiply by 10. So \(4.7 \text{ m} = 4.7 \times 100 = 470 \text{ cm}\).
Combining the Skills — Mixed and Real-Life Problems
Real-life problems may mix whole numbers and decimals with multipliers of 10, 100 or 1000. Always identify what you are multiplying and by which power of 10.
Key fact: × 10 → 1 place left | × 100 → 2 places left | × 1000 → 3 places left Applies to ALL numbers — whole and decimal.
Example 1: Unit conversion — \(3.5 \text{ km}\) to metres
Recall
1 km = 1,000 m, so multiply by 1000.
Calculate
\(3.5 \times 1000 = 3{,}500\)
Answer: 3,500 m
Example 2: A worker earns £8.50 per hour. How much over 100 hours?
Set up
\(8.50 \times 100\)
Shift 2 places left
\(8.50 \rightarrow 850\)
Answer: £850
Example 3: A medicine dose is 0.005 g. What is the dose in milligrams? (1 g = 1000 mg)
Set up
\(0.005 \times 1000\)
Shift 3 places left
\(0.005 \rightarrow 5\)
Answer: 5 mg
Example 4: A tile is 0.3 m wide. A room needs 10 tiles side by side. What is the total width?
Set up
\(0.3 \times 10\)
Shift 1 place left
\(0.3 \rightarrow 3\)
Answer: 3 m
Example 5: A can weighs 0.45 kg. A pallet holds 100 cans. What is the total weight?
Set up
\(0.45 \times 100\)
Shift 2 places left
\(0.45 \rightarrow 45\)
Answer: 45 kg
✓ Quick Check 3 — Mixed Applications
Question 1 of 10
Practice: Mixed Practice
Calculate each answer. Type your answer, then click Check.
#
Question
Answer
Result
1
36 × 100 =
2
0.8 × 10 =
3
0.45 × 100 =
4
7 × 1000 =
5
0.006 × 1000 =
6
12.5 × 10 =
7
0.07 × 100 =
8
450 × 100 =
9
0.003 × 1000 =
10
2.35 × 1000 =
⚠ Things to Watch Out For
Confusing the direction with dividing: Multiplying shifts digits LEFT (the number gets bigger). Dividing shifts digits RIGHT (the number gets smaller) — mixing these up is the most common error.
Just "adding zeros" fails for decimals: The rule is to shift every digit left, not simply tack zeros onto the end — this only happens to work by coincidence for whole numbers.
Miscounting the shifts: × 10 shifts 1 place, × 100 shifts 2 places, × 1000 shifts 3 places — count the zeros in the multiplier carefully.
Losing track of the decimal point: When multiplying a decimal, shift the decimal point itself the correct number of places rather than moving digits around it incorrectly.
Real-world unit conversions: Check you are multiplying (not dividing) by the correct power of 10 for the direction of the conversion, e.g. m to mm.