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

Question

____ x 10^ -2

Answer 1

To solve \(0.078 - (5.2 \times 10^{-3})\), we start by converting \(0.078\) into scientific notation.

We can express \(0.078\) as:

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

Now, we need to convert \(5.2 \times 10^{-3}\) into the same exponent as \(7.8 \times 10^{-2}\). We do this by expressing \(5.2 \times 10^{-3}\) with an exponent of \(-2\):

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

Now we perform the subtraction:

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

Calculating \(7.8 - 0.052\):

\[ 7.8 - 0.052 = 7.748 \]

Thus:

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

Now, to express this in standard scientific notation, we should adjust \(7.748\) to be between 1 and 10. We rewrite it:

\[ 7.748 = 0.7748 \times 10^{1} \]

Combining this with the original power of ten, we get:

\[ 0.7748 \times 10^{1} \times 10^{-2} = 0.7748 \times 10^{-1} \]

So, the answer in scientific notation is:

\[ 7.748 \times 10^{-2} = 0.7748 \times 10^{-1} \quad (if expressed in standard scientific notation format) \]

However, keeping the original phrasing:

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

Thus, you would write as \(7.748 , \text{x} , 10^{-2}\) if you follow the original prompt strictly using that notation.

Answer 2

Earth’s radius is approximately 3,959 miles, while Jupiter’s radius is approximately 4.3441×104 miles. How much bigger is Jupiter’s radius compared to Earth’s? Express your answer in scientific notation. Do not round your answer

Answer 3

To find out how much bigger Jupiter's radius is compared to Earth's, we first need to express both radii in scientific notation and perform the subtraction.

1. Earth's radius:

   • Given: 3,959 miles
   • In scientific notation: \[ 3,959 = 3.959 \times 10^3 \]

2. Jupiter's radius:

   • Given: \(4.3441 \times 10^4\) miles

To determine how much bigger Jupiter's radius is compared to Earth's, we perform the division of Jupiter's radius by Earth's radius:

\[ \text{Ratio} = \frac{\text{Jupiter's radius}}{\text{Earth's radius}} = \frac{4.3441 \times 10^4}{3.959 \times 10^3} \]

Now, let's break this calculation down:

Step 1: Calculate the coefficient: \[ \frac{4.3441}{3.959} \approx 1.096 \]

Step 2: Calculate the powers of ten: \[ \frac{10^4}{10^3} = 10^{4-3} = 10^1 \]

Now, combine these results: \[ \text{Ratio} \approx 1.096 \times 10^1 \]

Final Result: In scientific notation, considering \(1.096\) can be kept as is (as it is already between 1 and 10):

\[ \text{Ratio} = 1.096 \times 10^1 \]

Thus, Jupiter's radius is approximately:

\[ \boxed{1.096 \times 10^1} \]

This shows that Jupiter's radius is approximately \(10.96\) times larger than Earth's radius.