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Answer 1

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Answer 2

A national park covers an area earth, 1.42×10^6 acres. A nearby national forest covers an area of 1.2 x 10^6 acres. What is the total number of acres in the park and the forest combined?

Answer 3

To find the total area covered by the national park and the national forest combined, you simply add their areas together.

1. National park area: \( 1.42 \times 10^6 \) acres
2. National forest area: \( 1.2 \times 10^6 \) acres

Now, perform the addition:

\[ 1.42 \times 10^6 + 1.2 \times 10^6 = (1.42 + 1.2) \times 10^6 = 2.62 \times 10^6 \text{ acres} \]

Therefore, the total area in acres for the park and the forest combined is \( 2.62 \times 10^6 \) acres.

Answer 4

The distance from Venus to the sun is about 67,000,000 miles. The distance from earth to the sun is about 2.6 x 10^7 farther. What is the distance from earth to the sun? Write your answer in scientific notation to one decimal place.

Answer 5

To find the distance from Earth to the Sun, you need to add the distance from Venus to the Sun and the additional distance given.

1. Distance from Venus to the Sun: \( 67,000,000 \) miles
2. Distance from Earth to the Sun: \( 2.6 \times 10^7 \) miles

First, convert \( 67,000,000 \) miles into scientific notation:

\[ 67,000,000 = 6.7 \times 10^7 \text{ miles} \]

Now, add the two distances:

\[ \text{Distance from Earth to the Sun} = 6.7 \times 10^7 + 2.6 \times 10^7 \]

Combine the coefficients:

\[ (6.7 + 2.6) \times 10^7 = 9.3 \times 10^7 \text{ miles} \]

Thus, the distance from Earth to the Sun is \( 9.3 \times 10^7 \) miles.

Answer 6

Calculate.4.8 x 10^-3 - 9.4 x 10^6 . Express the answer in scientific notation rounding 2 decimal places.

Answer 7

To perform the calculation \( 4.8 \times 10^{-3} - 9.4 \times 10^{6} \), we first need to express both numbers in a way that allows us to subtract them. Typically, we can only directly subtract numbers that are in the same order of magnitude (i.e., the same power of 10).

In this case, \( 4.8 \times 10^{-3} \) is much smaller than \( 9.4 \times 10^{6} \). Since \( 9.4 \times 10^{6} \) is significantly greater than \( 4.8 \times 10^{-3} \), the result will be very close to \( 9.4 \times 10^{6} \).

To make the calculation easier, we can express \( 4.8 \times 10^{-3} \) in the same power of 10 as \( 9.4 \times 10^{6} \):

Convert \( 4.8 \times 10^{-3} \) to the exponent of \( 10^{6} \):

\[ 4.8 \times 10^{-3} = 4.8 \times 10^{-3} \times \frac{10^{6}}{10^{6}} = 4.8 \times 10^{6} \times 10^{-9} = 0.0000048 \times 10^{6} \]

Now we can now express it as:

\[ 0.0000048 \times 10^{6} = 4.8 \times 10^{-3} \]

Now, we can subtract:

\[ 9.4 \times 10^{6} - 0.0000048 \times 10^{6} \approx 9.4 \times 10^{6} \]

Since \( 4.8 \times 10^{-3} \) is negligible compared to \( 9.4 \times 10^{6} \), the difference remains approximately \( 9.4 \times 10^{6} \).

However, for exactness, we would calculate:

\[ 9.4 \times 10^{6} - 0.0000048 \times 10^{6} = (9.4 - 0.0000048) \times 10^{6} = 9.3999952 \times 10^{6} \]

Now rounding this to two decimal places:

\[ 9.40 \times 10^{6} \]

So, the final result is:

\[ \boxed{9.40 \times 10^{6}} \]

Answer 8

a strand of hair has an average mass of 2.17 x 10^-5 ounces. a grain of rice has an average mass of 0.002 ounces. How much heavier is a grain of rice than a strand of hair? Express your answer in scientific notation.

Answer 9

To find out how much heavier a grain of rice is than a strand of hair, we can subtract the mass of the strand of hair from the mass of the grain of rice.

1. Mass of a strand of hair: \( 2.17 \times 10^{-5} \) ounces
2. Mass of a grain of rice: \( 0.002 \) ounces

First, we need to express \( 0.002 \) ounces in scientific notation:

\[ 0.002 = 2.0 \times 10^{-3} \text{ ounces} \]

Now, we can perform the subtraction:

\[ \text{Difference} = \text{Mass of rice} - \text{Mass of hair} = (2.0 \times 10^{-3}) - (2.17 \times 10^{-5}) \]

Next, to perform the subtraction, we need to express both numbers in the same power of ten. It's easier to convert \( 2.0 \times 10^{-3} \) to have the same exponent as \( 2.17 \times 10^{-5} \).

Convert \( 2.0 \times 10^{-3} \):

\[ 2.0 \times 10^{-3} = 200.0 \times 10^{-5} \]

Now we can subtract:

\[ \text{Difference} = (200.0 \times 10^{-5}) - (2.17 \times 10^{-5}) = (200.0 - 2.17) \times 10^{-5} = 197.83 \times 10^{-5} \]

Now, we convert \( 197.83 \times 10^{-5} \) back into scientific notation:

\[ 197.83 \times 10^{-5} = 1.9783 \times 10^{-3} \]

Rounding \( 1.9783 \) to two decimal places gives us:

\[ 1.98 \times 10^{-3} \]

Thus, the mass by which a grain of rice is heavier than a strand of hair is:

\[ \boxed{1.98 \times 10^{-3}} \text{ ounces} \]

Answer 10

Light travels at an approximate rate of 1.9 x 10^5 mi./sec. There are about 3.2 x 10^7 seconds in a year. About how many miles does light travel in a year? Write the answer in scientific notation. Express the answer to the exact decimal place.

Answer 11

To calculate how far light travels in a year, we need to multiply the speed of light by the number of seconds in a year.

1. Speed of light: \( 1.9 \times 10^5 \) miles/second
2. Number of seconds in a year: \( 3.2 \times 10^7 \) seconds

Now, we multiply these two values together:

\[ \text{Distance} = \text{Speed} \times \text{Time} = (1.9 \times 10^5) \times (3.2 \times 10^7) \]

To perform the multiplication, we can multiply the coefficients and then add the exponents:

1. Multiply the coefficients: \( 1.9 \times 3.2 = 6.08 \)
2. Add the exponents: \( 10^5 \times 10^7 = 10^{5+7} = 10^{12} \)

Putting it all together, we have:

\[ \text{Distance} = 6.08 \times 10^{12} \text{ miles} \]

Therefore, the distance that light travels in a year is:

\[ \boxed{6.08 \times 10^{12}} \text{ miles} \]