**Writing a number in scientific notation worksheet :**

Worksheet on writing a number in scientific notation is much useful to the students who would like to practice problems on writing very large and very small numbers in scientific notation.

We can use the following techniques to write very large and small numbers in scientific notation.

1. The distance from Earth to the Sun is about 93,000,000 miles. Write this distance in scientific notation.

2. The average size of an atom is about 0.00000003 centimeter across. Write the average size of an atom in scientific notation.

3. When we write a number that is less than 1 in scientific notation, how does the power of 10 differ from when we write a number greater than 1 in scientific notation ?

**Question 1 : **

The distance from Earth to the Sun is about 93,000,000 miles. Write this distance in scientific notation.

**Solution : **

**Step 1 :**

Move the decimal point in 93,000,000 to the left until you have a number that is greater than or equal to 1 and less than 10.

Move the decimal point 7 places to the left.

Remove extra zeros.

9.3

**Step 2 :**

Divide the original number by the result from Step 1.

That is, divide 93,000,000 by 9.3.

10,000,000

Write your answer as a power of 10.

10⁷

**Step 3 :**

Write the product of the results from Steps 1 and 2.

Write a product to represent 93,000,000 in scientific notation.

93,000,000 = 9.3 × 10⁷ miles

**Question 2 : **

The average size of an atom is about 0.00000003 centimeter across. Write the average size of an atom in scientific notation.

**Solution : **

**Step 1 :**

Move the decimal point as many places as necessary to find a number that is greater than or equal to 1 and less than 10.

Place the decimal point after 3 and put one zero to make the decimal visible.

3.0

**Step 2 :**

Count the number of places you moved the decimal point.

8

**Step 2 :**

Multiply 3.0 times a power of 10.

Since 0.00000003 is less than 1, you moved the decimal point to the right and the exponent on 10 is negative.

3.0 × 10⁻⁸

The average size of an atom in scientific notation is 3.0 × 10⁻⁸.

**Question 3 : **

When we write a number that is less than 1 in scientific notation, how does the power of 10 differ from when we write a number greater than 1 in scientific notation ?

**Answer : **

The exponent is negative instead of positive.

After having gone through the stuff given above, we hope that the students would have understood, "Writing a number in scientific notation worksheet".

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