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Multiplying and Dividing by 10, 100, 1000
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Foundational Skills
Understand place value shift for ×10
\[ \times 10 \rightarrow \text{1 place right} \]
Decimal point moves right when multiplying by 10.
Understand place value shift for ÷10
\[ \div 10 \rightarrow \text{1 place left} \]
Decimal point moves left when dividing by 10.
Identify the effect of ×10 on a digit
\[ 2.5 \times 10: 5 \text{ moves where?} \]
Explain what happens to a specific digit.
Identify the effect of ÷10 on a digit
\[ 45 \div 10: 5 \text{ moves where?} \]
Explain what happens to a specific digit.
Multiplying by 10
Multiply an integer by 10
\[ 34 \times 10 = 340 \]
Multiply a whole number by 10.
Multiply a 1dp decimal by 10
\[ 3.5 \times 10 = 35 \]
NOT 3.50 – the decimal point moves!
Multiply a 2dp decimal by 10
\[ 4.56 \times 10 = 45.6 \]
Answer has one decimal place.
Multiply a 3dp decimal by 10
\[ 2.345 \times 10 = 23.45 \]
Answer has two decimal places.
Multiply a decimal less than 1 by 10
\[ 0.7 \times 10 = 7 \]
Result becomes a whole number.
Multiplying by 100
Multiply an integer by 100
\[ 45 \times 100 = 4500 \]
Multiply a whole number by 100.
Multiply a 1dp decimal by 100
\[ 2.5 \times 100 = 250 \]
Answer becomes a whole number.
Multiply a 2dp decimal by 100
\[ 3.45 \times 100 = 345 \]
Answer becomes a whole number.
Multiply a 3dp decimal by 100
\[ 1.234 \times 100 = 123.4 \]
Answer has one decimal place.
Multiply a small decimal by 100
\[ 0.08 \times 100 = 8 \]
Hundredths become ones.
Multiplying by 1000
Multiply an integer by 1000
\[ 7 \times 1000 = 7000 \]
Multiply a whole number by 1000.
Multiply a 1dp decimal by 1000
\[ 2.5 \times 1000 = 2500 \]
Answer has extra zeros.
Multiply a 2dp decimal by 1000
\[ 3.45 \times 1000 = 3450 \]
Answer becomes a whole number.
Multiply a 3dp decimal by 1000
\[ 1.234 \times 1000 = 1234 \]
All decimal places disappear.
Dividing by 10
Divide an integer by 10
\[ 45 \div 10 = 4.5 \]
Result may have decimal places.
Divide a 1dp decimal by 10
\[ 3.5 \div 10 = 0.35 \]
Answer has 2 decimal places.
Divide a 2dp decimal by 10
\[ 4.56 \div 10 = 0.456 \]
Answer has 3 decimal places.
Divide a decimal less than 1 by 10
\[ 0.5 \div 10 = 0.05 \]
Number gets even smaller.
Divide a small decimal by 10
\[ 0.04 \div 10 = 0.004 \]
Very small result with many zeros.
Dividing by 100
Divide an integer by 100
\[ 350 \div 100 = 3.5 \]
Result may have decimal places.
Divide a 1dp decimal by 100
\[ 4.5 \div 100 = 0.045 \]
Answer has 3 decimal places.
Divide a 2dp decimal by 100
\[ 3.45 \div 100 = 0.0345 \]
Answer has 4 decimal places.
Divide a decimal less than 1 by 100
\[ 0.6 \div 100 = 0.006 \]
Very small result.
Dividing by 1000
Divide an integer by 1000
\[ 4500 \div 1000 = 4.5 \]
Result may have decimal places.
Divide a 1dp decimal by 1000
\[ 5.5 \div 1000 = 0.0055 \]
Very small result.
Divide a 2dp decimal by 1000
\[ 3.45 \div 1000 = 0.00345 \]
Answer has 5 decimal places.
Mixed Operations
Choose multiply or divide to solve
\[ 0.5 \rightarrow 50: \times \text{ or } \div \text{?} \]
Identify the correct operation.
Find the missing power of 10
\[ 3.5 \times \square = 350 \]
Find 10, 100, or 1000.
Solve multi-step with powers of 10
\[ 4.5 \times 10 \div 100 = \square \]
Chain multiple operations.
Special Cases
Multiply to create integer from decimal
\[ 0.25 \times \square = 25 \]
Find the multiplier.
Divide to create decimal from integer
\[ 250 \div \square = 2.5 \]
Find the divisor.
Understand effect of ×10 and ÷10 together
\[ 5.5 \times 10 \div 10 = \square \]
Inverse operations cancel out.
Compare results of different operations
\[ 3.5 \times 10 \text{ vs } 35 \div 10 \]
Which is larger?
Timer (Optional)
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