The image presents five problems related to scientific notation. 1. Convert $97,030,000,000$ to scientific notation.
2025/4/30
1. Problem Description
The image presents five problems related to scientific notation.
1. Convert $97,030,000,000$ to scientific notation.
2. Convert $2.9 \times 10^{-6}$ to standard form.
3. Simplify $(6.5 \times 10^{-5})(3.2 \times 10^{-4})$ and write the answer in scientific notation.
4. Simplify $(1.25 \times 10^8) - (9.4 \times 10^7)$ and write the answer in scientific notation and standard form.
5. Lake Superior is $3.17 \times 10^4$ square miles while Lake Ontario is $7.3 \times 10^3$ square miles. Approximately how many times greater than Lake Ontario is Lake Superior? Write your answer in standard form.
2. Solution Steps
1. To write $97,030,000,000$ in scientific notation, we move the decimal point 10 places to the left to get $9.703$. Then multiply by $10^{10}$.
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2. To write $2.9 \times 10^{-6}$ in standard form, we move the decimal point 6 places to the left.
3. To simplify $(6.5 \times 10^{-5})(3.2 \times 10^{-4})$, we multiply the numbers and add the exponents:
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To write the answer in scientific notation, we rewrite as .
So we have .
4. To simplify $(1.25 \times 10^8) - (9.4 \times 10^7)$, we first make the exponents the same. We can write $9.4 \times 10^7$ as $0.94 \times 10^8$.
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To write in scientific notation, we rewrite as .
In standard form, this is .
5. To find how many times greater Lake Superior is than Lake Ontario, we divide the area of Lake Superior by the area of Lake Ontario:
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Since the problem asks for the answer in standard form and "approximately", we can round this to .