Calculate 6.25×106−4.73×106 . Express your answer in scientific notation to 2 decimal places.

Answer 1

To calculate \( 6.25 \times 10^6 - 4.73 \times 10^6 \), we first recognize that both terms are in the form of \( a \times 10^n \), where \( n = 6 \).

We can subtract the coefficients (the \( a \) values) while keeping the common power of ten:

\[ (6.25 - 4.73) \times 10^6 \]

Calculating the difference of the coefficients:

\[ 6.25 - 4.73 = 1.52 \]

Thus, we have:

\[ 1.52 \times 10^6 \]

Now, we need to express our answer in scientific notation, ensuring it is to 2 decimal places.

The final answer is:

\[ \boxed{1.52 \times 10^6} \]

Answer 2

The average distance from Earth to Mars is 2.25×108 km, and the distance from Earth to Neptune is 4.3514×109 km. How much farther is Neptune from Earth than Mars? Express your answer in scientific notation. Do not round your answer

Answer 3

To find out how much farther Neptune is from Earth than Mars, we need to subtract the distance from Earth to Mars from the distance from Earth to Neptune:

\[ 4.3514 \times 10^9 \text{ km} - 2.25 \times 10^8 \text{ km} \]

First, we will express both distances in a way that makes the subtraction easier. We can express \( 2.25 \times 10^8 \) in terms of \( 10^9 \):

\[ 2.25 \times 10^8 = 0.225 \times 10^9 \]

Now we can rewrite the subtraction:

\[ 4.3514 \times 10^9 - 0.225 \times 10^9 \]

Now, we can perform the subtraction:

\[ (4.3514 - 0.225) \times 10^9 = 4.1264 \times 10^9 \]

Thus, the distance that Neptune is farther away from Earth than Mars is:

\[ \boxed{4.1264 \times 10^9} \text{ km} \]

Answer 4

Human hair grows at a rate of about 6.849×10−4 cm per hour to 2.329×10−2 cm per hour. The rate depends on gender, genetics, age, and health. Find the difference between the high end and the low end of the range. Express your answer in scientific notation. Do not round your answer

Answer 5

To find the difference between the high end \( 2.329 \times 10^{-2} \) cm per hour and the low end \( 6.849 \times 10^{-4} \) cm per hour, we perform the subtraction:

\[ 2.329 \times 10^{-2} - 6.849 \times 10^{-4} \]

First, we convert \( 6.849 \times 10^{-4} \) to have the same exponent as \( 2.329 \times 10^{-2} \). We do this by expressing it as:

\[ 6.849 \times 10^{-4} = 0.06849 \times 10^{-2} \]

Now we can rewrite the subtraction:

\[ 2.329 \times 10^{-2} - 0.06849 \times 10^{-2} \]

Now, subtract the coefficients:

\[ (2.329 - 0.06849) \times 10^{-2} = 2.26051 \times 10^{-2} \]

Finally, we express this result in scientific notation. The final answer is:

\[ \boxed{2.26051 \times 10^{-2}} \text{ cm per hour} \]

Answer 6

Find 0.078−(5.2×10−3) . Express your answer in scientific notation. Do not round your answer.

Answer 7

To find the result of \( 0.078 - (5.2 \times 10^{-3}) \), we first need to express \( 0.078 \) in a form with the same exponent for easier subtraction.

Convert \( 0.078 \) to scientific notation:

\[ 0.078 = 7.8 \times 10^{-2} \]

Now, we perform the subtraction:

\[ 7.8 \times 10^{-2} - 5.2 \times 10^{-3} \]

Next, we need to express \( 5.2 \times 10^{-3} \) with the same exponent as \( 7.8 \times 10^{-2} \). We can convert \( 5.2 \times 10^{-3} \) to \( 0.052 \times 10^{-2} \):

\[ 5.2 \times 10^{-3} = 0.052 \times 10^{-2} \]

Now we can rewrite the subtraction:

\[ 7.8 \times 10^{-2} - 0.052 \times 10^{-2} \]

Now, subtract the coefficients:

\[ (7.8 - 0.052) \times 10^{-2} = 7.748 \times 10^{-2} \]

The final answer in scientific notation is:

\[ \boxed{7.748 \times 10^{-2}} \]