Movement of the Decimal Point
Table Of Contents
🎬 Math Angel Video: Decimal Shifting Rules Explained
Multiplying and Dividing Decimals by 10, 100, 1000
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🛎️ How to Multiply Decimals by Powers of 10?
When multiplying a number by 10, 100, or 1000, move the decimal point 1, 2, or 3 places to the right, respectively. For example:
- $12.34 \times 10 = 123.4$Â Â (move 1 place)
- $12.34 \times 100 = 1234$Â Â (move 2 places)
- $12.34 \times 1000 = 12340$Â Â (move 3 places)
❇️ Moving the decimal point to the right makes the number larger.
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🛎️ How to Divide Decimals by Powers of 10?
When dividing a number by 10, 100, or 1000, move the decimal point 1, 2, or 3 places to the left, respectively. For example:
- $12.34 \div 10 = 1.234$Â Â (move 1 place)
- $12.34 \div 100 = 0.1234$Â Â (move 2 places)
- $12.34 \div 1000 = 0.01234$Â Â (move 3 places)
❇️ Moving the decimal point left makes the number smaller.
How to Move the Decimal Point (Examples)
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- Multiplication by 1000 means moving the decimal point 3 places to the right.
$$5.02 \times 1000 = 5020$$
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- Division by 100 means moving the decimal point 2 places to the left.
$$4.21 \div 100 = 0.0421$$
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To convert a percentage to a decimal, divide by 100.
$$56.7\% = \frac{56.7}{100} = 0.567$$Then, multiplying by 10 means moving the decimal point 1 place to the right.
$$0.567 \times 10 = 5.67$$
Shifting the Decimal Point to Convert Between Units
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To convert 2.8 meters to centimeters, multiply by 100 because 1 m = 100 cm.
- $2.8 \times 100 = 280$
- Therefore, 2.8 m is equal to 280 cm.
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To convert 2.8 meters to kilometers, divide by 1000 because 1 m = $\frac{1}{1000}$ km.
- $2.8 \div 1000 = 0.0028$
- Therefore, 2.8 m is equal to 0.0028 km.
🍪 Quiz: Practice Decimal Place Movement
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