**Scientific notation worksheet :**

Worksheet on scientific notation is much useful to the students who would like to practice problems on writing very large or very small numbers using scientific notation.

Write each number in scientific notation.

1) 0.00006

2) 5400000

3) 71 x 10²

4) 33 x 10⁻³

5) 0.63 x 10⁻³

6) 0.000216

7) 0.0000009

8) 804 x 10²

9) 4.8

10) 0.99 x 10¹

**Question 1 :**

Write the given number in scientific notation.

0.00006

**Solution :**

Here decimal point comes first at non zero digit comes next.

We have to move the decimal point to the right.

No. of digits from decimal point up to the first non zero digit = 5

So, the decimal point has to be moved 5 digits to the right and exponent of 10 should be -5 (negative integer)

Hence, 0.00006 = 6 x 10⁻⁵.

**Question 2 :**

Write the given number in scientific notation.

5400000

**Solution :**

Here we don't find decimal point in 5400000. So we have to assume that there is decimal point at the end .

Then, 5400000 ---------> 5400000.

Here non zero digit comes first and decimal point comes next.

We have to move the decimal point to the left.

No. of digits between the 1st non zero digit and decimal point = 6

So, the decimal point has to be moved 6 digits to the left and exponent of 10 should be 6 (positive integer)

5400000 = 5.400000 x 10⁶ = 5.4 x 10⁶

Hence, 5400000 = 5.4 x 10⁶

(Here zeros after the decimal point are not taken. Because, they are not valid zeros)

**Question 3 :**

Write the given number in scientific notation.

71 x 10²

**Solution :**

Here we don't find decimal point in 71x 10². So we have to assume that there is decimal point at the end of 71

Then, 71x 10² ---------> 71. x 10²

Here non zero digit comes first and decimal point comes next.

We have to move the decimal point to the left.

No. of digits between the 1st non zero digit and decimal point = 1

So, the decimal point has to be moved 1 digit to the left and exponent of 10 should be 1 (positive integer)

71. x 10² = 7.1 x 10¹ x 10²

71. x 10² = 7.1 x 10³

Hence, 71 x 10² = 7.1 x 10³

**Question 4 :**

Write the given number in scientific notation.

33 x 10⁻³

**Solution :**

Here we don't find decimal point in 33 x 10⁻³ So we have to assume that there is decimal point at the end of 33

Then, 33x 10⁻³ ---------> 33. x 10⁻³

Here non zero digit comes first and decimal point comes next.

We have to move the decimal point to the left.

No. of digits between the 1st non zero digit and decimal point = 1

So, the decimal point has to be moved 1 digit to the left and exponent of 10 should be 1 (positive integer)

33. x 10⁻³ = 3.3 x 10¹ x 10⁻³

33. x 10⁻³ = 3.3 x 10⁻²

Hence, 33x 10⁻³ = 3.3 x 10⁻²

**Question 5 :**

Write the given number in scientific notation.

0.63 x 10⁻³

**Solution : **

Here decimal point comes first and non zero digit comes next.

We have to move the decimal point to the right.

No. of digits from decimal point up to the first non zero digit = 1

So, the decimal point has to be moved 1 digit to the right and exponent of 10 should be -1 (negative integer)

0.63 x 10⁻³ = 6.3 x 10⁻¹ x 10⁻³

0.63 x 10⁻³ = 6.3 x 10⁻⁴

Hence, 0.63 x 10⁻³ = 6.3 x 10⁻⁴

**Question 6 :**

Write the given number in scientific notation.

0.000216

**Solution : **

Here decimal point comes first and non zero digit comes next.

We have to move the decimal point to the right.

No. of digits from decimal point up to the first non zero digit = 4

So, the decimal point has to be moved 4 digits to the right and exponent of 10 should be -4 (negative integer)

0.000216 = 2.16 x 10⁻⁴

Hence, 0.000216 = 2.16 x 10⁻⁴

**Question 7 :**

Write the given number in scientific notation.

0.0000009

**Solution : **

Here decimal point comes first and non zero digit comes next.

We have to move the decimal point to the right.

No. of digits from decimal point up to the first non zero digit = 7

So, the decimal point has to be moved 7 digits to the right and exponent of 10 should be -7 (negative integer)

0.0000009 = 9 x 10⁻⁷

Hence, 0.0000009 = 9 x 10⁻⁷

**Question 8 :**

Write the given number in scientific notation.

804 x 10²

**Solution :**

Here we don't find decimal point in 804 x 10² . So we have to assume that there is decimal point at the end .

Then, 804 x 10² ---------> 804. x 10²

Here non zero digit comes first and decimal point comes next.

We have to move the decimal point to the left.

No. of digits between the 1st non zero digit and decimal point = 2

So, the decimal point has to be moved 2 digits to the left and exponent of 10 should be 2 (positive integer)

804. x 10² = 8.04 x 10² x 10²

804. x 10² = 8.04 x 10⁴

Hence, 804 x 10² = 8.04 x 10⁴

**Question 9 :**

Write the given number in scientific notation.

4.8

**Solution :**

Here the given number is almost in scientific notation.

Because there is only one non zero digit before the decimal point.

We don't have to move the decimal point either to the left or right.

Then, exponent of 10 should be zero.

4.8 = 4.8 x 10⁰

Hence, 4.8 = 4.8 x 10⁰

**Question 10 :**

Write the given number in scientific notation.

0.99 x 10¹

**Solution : **

Here decimal point comes first and non zero digit comes next.

We have to move the decimal to the right.

No. of digits from decimal point up to the first non zero digit = 1

So, the decimal point has to be moved 1 digit to the right and exponent of 10 should be -1 (negative integer)

0.99 x 10¹ = 9.9 x 10⁻¹ x 10¹

0.99 x 10⁻¹ = 9.9 x 10⁰

Hence, 0.99 x 10⁻¹ = 9.9 x 10⁰

After having gone through the stuff and examples, we hope that the students would have understood "Scientific notation worksheet".

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