Question

ASTRONOMY The average distance from Mercury to the Sun is 35,980,000 miles. Express this distance in scientific notation.

Short answer

$35980000$Can be written in scientific notation as $\mathbf{3}\mathbf{.}\mathbf{598}\times {\mathbf{10}}^7$.

Step-by-step solution

Step 1. Write steps to convert standard form to scientific notations.

1. Move decimal point to the right until it is the first nonzero digit. It is a real number x.

2. Count the numbers of decimal places m and direction in which decimal point is moved.

3. If the decimal point is moved towards right then write the number as$x\times {10}^{-m}$ and if the decimal point is moved towards left then write the number as $x\times {10}^m$. Remove the unnecessary zeros.

Step 2. Apply steps to convert standard form to scientific notation.

Move decimal point towards left till it reaches first nonzero number and then count the number of decimal places.

$35980000\to 3.5980000$

Number of decimal places, $m=7$.

Step 3. Write a given number in scientific notation.

As the decimal point is moved towards the left, write the number as $x\times {10}^m$.

$3.598\times {10}^7$

Therefore,$35980000$ can be written in scientific notation as $3.598\times {10}^7$.