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

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 $10^{10}$.

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

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

$2.9 \times 10^{-6} = 0.0000029$

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

$(6.5 \times 3.2) \times (10^{-5} \times 10^{-4}) = 20.8 \times 10^{-9}$.

To write the answer in scientific notation, we rewrite $20.8$ as $2.08 \times 10^1$.

So we have $(2.08 \times 10^1) \times 10^{-9} = 2.08 \times 10^{-8}$.

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 $0.94 \times 10^8$.

$(1.25 \times 10^8) - (0.94 \times 10^8) = (1.25 - 0.94) \times 10^8 = 0.31 \times 10^8$.

To write in scientific notation, we rewrite $0.31 \times 10^8$ as $3.1 \times 10^7$.

In standard form, this is $31,000,000$.

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:

$\frac{3.17 \times 10^4}{7.3 \times 10^3} = \frac{3.17}{7.3} \times \frac{10^4}{10^3} \approx 0.434 \times 10^1 = 4.34$.

Since the problem asks for the answer in standard form and "approximately", we can round this to $4.3$.

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. $4.3$