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Multiplying Decimals by Exponents (Hard) — Easy Worksheet 2
Grade 8 · Whoobee Name: ____________________ Date: __________
Solve each problem. Write answers as decimals or in scientific notation where indicated. Show no commas.
How to solve
To multiply a decimal by 10n, move the decimal point n places to the right (positive n) or left (negative n). For (0.5)3, multiply 0.5 × 0.5 × 0.5 = 0.125. To multiply numbers in scientific notation, multiply the coefficients and add the exponents: (3.2 × 104) × (2.5 × 10-2) = 8.0 × 102 = 800. If the coefficient reaches 10, adjust: 12 × 103 = 1.2 × 104.
Example
5 × 10-2 = ___
Answer: 0.05
Not quite. The answer is
💡 Multiplying 8.6 by 10-3 moves the decimal point 3 places left, making the number smaller. Fill any empty places with zeros. So 8.6 × 10−3 = 0.0086.
✓ Correct!
Not quite. The answer is
💡 Multiplying 8.6 by 10-3 moves the decimal point 3 places left, making the number smaller. Fill any empty places with zeros. So 8.6 × 10−3 = 0.0086.
💡 How to solve: Multiplying Decimals by Exponents (Hard)
To multiply a decimal by 10n, move the decimal point n places to the right (positive n) or left (negative n). For (0.5)3, multiply 0.5 × 0.5 × 0.5 = 0.125. To multiply numbers in scientific notation, multiply the coefficients and add the exponents: (3.2 × 104) × (2.5 × 10-2) = 8.0 × 102 = 800. If the coefficient reaches 10, adjust: 12 × 103 = 1.2 × 104.
Try a similar one
4.3 × 10-2 = ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 (0.5)2 means 0.5 × 0.5. Multiply the digits as whole numbers: 5 × 5 = 25. Count the decimal places in the factors: 1 + 1 = 2, so the product has 2 decimal places: 0.25.
✓ Correct!
Not quite. The answer is
💡 (0.5)2 means 0.5 × 0.5. Multiply the digits as whole numbers: 5 × 5 = 25. Count the decimal places in the factors: 1 + 1 = 2, so the product has 2 decimal places: 0.25.
💡 How to solve: Multiplying Decimals by Exponents (Hard)
To multiply a decimal by 10n, move the decimal point n places to the right (positive n) or left (negative n). For (0.5)3, multiply 0.5 × 0.5 × 0.5 = 0.125. To multiply numbers in scientific notation, multiply the coefficients and add the exponents: (3.2 × 104) × (2.5 × 10-2) = 8.0 × 102 = 800. If the coefficient reaches 10, adjust: 12 × 103 = 1.2 × 104.
Try a similar one
1.3 × 10-2 = ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Multiply the number parts: 2 × 4 = 8. Add the exponents: 2 + 2 = 4. That gives 8 × 104. 8 is between 1 and 10, so the answer is 8 × 104.
✓ Correct!
Not quite. The answer is
💡 Multiply the number parts: 2 × 4 = 8. Add the exponents: 2 + 2 = 4. That gives 8 × 104. 8 is between 1 and 10, so the answer is 8 × 104.
💡 How to solve: Multiplying Decimals by Exponents (Hard)
To multiply a decimal by 10n, move the decimal point n places to the right (positive n) or left (negative n). For (0.5)3, multiply 0.5 × 0.5 × 0.5 = 0.125. To multiply numbers in scientific notation, multiply the coefficients and add the exponents: (3.2 × 104) × (2.5 × 10-2) = 8.0 × 102 = 800. If the coefficient reaches 10, adjust: 12 × 103 = 1.2 × 104.
Try a similar one
8.6 × 10-4 = ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Multiplying 0.057 by 104 moves the decimal point 4 places right, making the number bigger. Fill any empty places with zeros. So 0.057 × 104 = 570.
✓ Correct!
Not quite. The answer is
💡 Multiplying 0.057 by 104 moves the decimal point 4 places right, making the number bigger. Fill any empty places with zeros. So 0.057 × 104 = 570.
💡 How to solve: Multiplying Decimals by Exponents (Hard)
To multiply a decimal by 10n, move the decimal point n places to the right (positive n) or left (negative n). For (0.5)3, multiply 0.5 × 0.5 × 0.5 = 0.125. To multiply numbers in scientific notation, multiply the coefficients and add the exponents: (3.2 × 104) × (2.5 × 10-2) = 8.0 × 102 = 800. If the coefficient reaches 10, adjust: 12 × 103 = 1.2 × 104.
Try a similar one
3.7 × 10-4 = ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Count how many places the decimal point moves to turn 4 into 4000. It moves 3 places right, so n is positive. So n = 3.
✓ Correct!
Not quite. The answer is
💡 Count how many places the decimal point moves to turn 4 into 4000. It moves 3 places right, so n is positive. So n = 3.
💡 How to solve: Multiplying Decimals by Exponents (Hard)
To multiply a decimal by 10n, move the decimal point n places to the right (positive n) or left (negative n). For (0.5)3, multiply 0.5 × 0.5 × 0.5 = 0.125. To multiply numbers in scientific notation, multiply the coefficients and add the exponents: (3.2 × 104) × (2.5 × 10-2) = 8.0 × 102 = 800. If the coefficient reaches 10, adjust: 12 × 103 = 1.2 × 104.
Try a similar one
2.5 × 10-4 = ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Work out the power first: (0.2)2 = 0.2 × 0.2. Multiply the digits as whole numbers: 2 × 2 = 4. Count the decimal places in the factors: 1 + 1 = 2, so the product has 2 decimal places: 0.04. Multiplying 0.04 by 104 moves the decimal point 4 places right, making the number bigger. Fill any empty places with zeros. So (0.2)2 × 104 = 400.
✓ Correct!
Not quite. The answer is
💡 Work out the power first: (0.2)2 = 0.2 × 0.2. Multiply the digits as whole numbers: 2 × 2 = 4. Count the decimal places in the factors: 1 + 1 = 2, so the product has 2 decimal places: 0.04. Multiplying 0.04 by 104 moves the decimal point 4 places right, making the number bigger. Fill any empty places with zeros. So (0.2)2 × 104 = 400.
💡 How to solve: Multiplying Decimals by Exponents (Hard)
To multiply a decimal by 10n, move the decimal point n places to the right (positive n) or left (negative n). For (0.5)3, multiply 0.5 × 0.5 × 0.5 = 0.125. To multiply numbers in scientific notation, multiply the coefficients and add the exponents: (3.2 × 104) × (2.5 × 10-2) = 8.0 × 102 = 800. If the coefficient reaches 10, adjust: 12 × 103 = 1.2 × 104.
Try a similar one
6.2 × 10-4 = ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 First multiply the decimals: 0.075 × 8. Multiply the digits as whole numbers: 75 × 8 = 600. Count the decimal places in the factors: 3, so the product has 3 decimal places: 0.600, which is the same as 0.6. Multiplying 0.6 by 104 moves the decimal point 4 places right, making the number bigger. Fill any empty places with zeros. So 0.075 × 8 × 104 = 6000.
✓ Correct!
Not quite. The answer is
💡 First multiply the decimals: 0.075 × 8. Multiply the digits as whole numbers: 75 × 8 = 600. Count the decimal places in the factors: 3, so the product has 3 decimal places: 0.600, which is the same as 0.6. Multiplying 0.6 by 104 moves the decimal point 4 places right, making the number bigger. Fill any empty places with zeros. So 0.075 × 8 × 104 = 6000.
💡 How to solve: Multiplying Decimals by Exponents (Hard)
To multiply a decimal by 10n, move the decimal point n places to the right (positive n) or left (negative n). For (0.5)3, multiply 0.5 × 0.5 × 0.5 = 0.125. To multiply numbers in scientific notation, multiply the coefficients and add the exponents: (3.2 × 104) × (2.5 × 10-2) = 8.0 × 102 = 800. If the coefficient reaches 10, adjust: 12 × 103 = 1.2 × 104.
Try a similar one
3.9 × 10-2 = ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Move the decimal point left until only one nonzero digit is in front of it: 3. It moved 4 places left, so the power of 10 is 4. So 30,000 = 3 × 104.
✓ Correct!
Not quite. The answer is
💡 Move the decimal point left until only one nonzero digit is in front of it: 3. It moved 4 places left, so the power of 10 is 4. So 30,000 = 3 × 104.
💡 How to solve: Multiplying Decimals by Exponents (Hard)
To multiply a decimal by 10n, move the decimal point n places to the right (positive n) or left (negative n). For (0.5)3, multiply 0.5 × 0.5 × 0.5 = 0.125. To multiply numbers in scientific notation, multiply the coefficients and add the exponents: (3.2 × 104) × (2.5 × 10-2) = 8.0 × 102 = 800. If the coefficient reaches 10, adjust: 12 × 103 = 1.2 × 104.
Try a similar one
2.7 × 10-2 = ___
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Multiplying Decimals by Exponents (Hard) — Easy Worksheet 2
Solve each problem. Write answers as decimals or in scientific notation where indicated. Show no commas.