Explanation:
We need to simplify each expression and write the answer in scientific notation, which means a number between 1 and 10 (not including 10) multiplied by a power of 10.
Let’s go problem by problem:
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Problem 1: $(7 \times 10^8)(9 \times 10^6)$
Multiply coefficients: $7 \times 9 = 63$
Add exponents: $10^8 \times 10^6 = 10^{8+6} = 10^{14}$
So we get: $63 \times 10^{14}$
But 63 is not between 1 and 10 → convert:
$63 = 6.3 \times 10^1$, so
$63 \times 10^{14} = 6.3 \times 10^1 \times 10^{14} = 6.3 \times 10^{15}$
✔ Answer:
6.3 × 10¹⁵
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Problem 2: $\frac{3 \times 10^4}{8 \times 10}$
Note: $10 = 10^1$, so denominator is $8 \times 10^1$
Divide coefficients: $3 ÷ 8 = 0.375$
Subtract exponents: $10^4 ÷ 10^1 = 10^{4-1} = 10^3$
So: $0.375 \times 10^3$
But 0.375 is less than 1 → convert to scientific notation:
$0.375 = 3.75 \times 10^{-1}$
Then: $3.75 \times 10^{-1} \times 10^3 = 3.75 \times 10^{2}$
✔ Answer:
3.75 × 10²
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Problem 3: $\frac{4 \times 10^9}{5 \times 10^7}$
Coefficients: $4 ÷ 5 = 0.8$
Exponents: $10^9 ÷ 10^7 = 10^{2}$
So: $0.8 \times 10^2$
Convert: $0.8 = 8 \times 10^{-1}$
Then: $8 \times 10^{-1} \times 10^2 = 8 \times 10^{1}$
✔ Answer:
8 × 10¹
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Problem 4: $(2 \times 10^3)(3 \times 10^4)$
Coefficients: $2 × 3 = 6$
Exponents: $10^3 × 10^4 = 10^7$
So: $6 × 10^7$ — already in scientific notation (6 is between 1 and 10).
✔ Answer:
6 × 10⁷
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Problem 5: $(3 \times 10^7)(9 \times 10^6)$
Coefficients: $3 × 9 = 27$
Exponents: $10^7 × 10^6 = 10^{13}$
So: $27 × 10^{13}$
Convert: $27 = 2.7 × 10^1$
→ $2.7 × 10^1 × 10^{13} = 2.7 × 10^{14}$
✔ Answer:
2.7 × 10¹⁴
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Problem 6: $\frac{4 \times 10^5}{16 \times 10^2}$
Coefficients: $4 ÷ 16 = 0.25$
Exponents: $10^5 ÷ 10^2 = 10^3$
So: $0.25 × 10^3$
Convert: $0.25 = 2.5 × 10^{-1}$
→ $2.5 × 10^{-1} × 10^3 = 2.5 × 10^2$
✔ Answer:
2.5 × 10²
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Problem 7: $\frac{9 \times 10^5}{10 \times 10^3}$
Denominator: $10 × 10^3 = 10^1 × 10^3 = 10^4$
So expression becomes: $\frac{9 × 10^5}{10^4} = 9 × 10^{5-4} = 9 × 10^1$
Already scientific notation.
✔ Answer:
9 × 10¹
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Problem 8: $(11 \times 10^4)(7 \times 10^2)$
Coefficients: $11 × 7 = 77$
Exponents: $10^4 × 10^2 = 10^6$
So: $77 × 10^6$
Convert: $77 = 7.7 × 10^1$
→ $7.7 × 10^1 × 10^6 = 7.7 × 10^7$
✔ Answer:
7.7 × 10⁷
Now double-check all answers for correctness:
1) 6.3 × 10¹⁵ ✔
2) 3.75 × 10² ✔
3) 8 × 10¹ ✔
4) 6 × 10⁷ ✔
5) 2.7 × 10¹⁴ ✔
6) 2.5 × 10² ✔
7) 9 × 10¹ ✔
8) 7.7 × 10⁷ ✔
All correct.
Final Answer:
1) 6.3
2) 3.75
3) 8
4) 6
5) 2.7
6) 2.5
7) 9
8) 7.7
Parent Tip: Review the logic above to help your child master the concept of scientific notation multiplication and division worksheet.
