The image presents five problems related to scientific notation. 1. Convert $97,030,000,000$ to scientific notation.

ArithmeticScientific NotationExponentsDecimal OperationsApproximation
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 $10^{10}$.

97,030,000,000=9.703×101097,030,000,000 = 9.703 \times 10^{10}.

2. To write $2.9 \times 10^{-6}$ in standard form, we move the decimal point 6 places to the left.

2.9×106=0.00000292.9 \times 10^{-6} = 0.0000029

3. To simplify $(6.5 \times 10^{-5})(3.2 \times 10^{-4})$, we multiply the numbers and add the exponents:

(6.5×3.2)×(105×104)=20.8×109(6.5 \times 3.2) \times (10^{-5} \times 10^{-4}) = 20.8 \times 10^{-9}.
To write the answer in scientific notation, we rewrite 20.820.8 as 2.08×1012.08 \times 10^1.
So we have (2.08×101)×109=2.08×108(2.08 \times 10^1) \times 10^{-9} = 2.08 \times 10^{-8}.

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 $0.94 \times 10^8$.

(1.25×108)(0.94×108)=(1.250.94)×108=0.31×108(1.25 \times 10^8) - (0.94 \times 10^8) = (1.25 - 0.94) \times 10^8 = 0.31 \times 10^8.
To write in scientific notation, we rewrite 0.31×1080.31 \times 10^8 as 3.1×1073.1 \times 10^7.
In standard form, this is 31,000,00031,000,000.

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:

3.17×1047.3×103=3.177.3×1041030.434×101=4.34\frac{3.17 \times 10^4}{7.3 \times 10^3} = \frac{3.17}{7.3} \times \frac{10^4}{10^3} \approx 0.434 \times 10^1 = 4.34.
Since the problem asks for the answer in standard form and "approximately", we can round this to 4.34.3.

3. Final Answer

1. $9.703 \times 10^{10}$

2. $0.0000029$

3. $2.08 \times 10^{-8}$

4. Scientific notation: $3.1 \times 10^7$; Standard form: $31,000,000$

5. $4.3$

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