**Scientific Notation Worksheet :**

Worksheet given in this section will be much useful to the students who would like to practice problems on scientific notation.

Before look at the worksheet, if you would like to learn the stuff scientific notation rules,

**Problem 1 :**

Write the given number in scientific notation.

0.00006

**Problem 2 :**

Write the given number in scientific notation.

5400000

**Problem 3 : **

Write the given number in scientific notation.

71 x 10^{2}

**Problem 4 :**

Write the given number in scientific notation.

33 x 10^{-3}

**Problem 5 :**

Write the given number in scientific notation.

0.63 x 10^{-3}

**Problem 6 :**

Write the given number in scientific notation.

0.000216

**Problem 7 :**

Write the given number in scientific notation.

0.0000009

**Problem 8 :**

Write the given number in scientific notation.

804 x 10^{2}

**Problem 9 :**

Write the given number in scientific notation.

4.8

**Problem 10 :**

Write the given number in scientific notation.

0.99 x 10^{1}

**Problem 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 the decimal point up to the first non zero digit is 5.

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

Hence, the scientific notation of 0.00006 is

6 x 10^{-5}

**Problem 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 the decimal point is 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 10^{6}

5400000 = 5.4 x 10^{6}

Hence, the scientific notation of 5400000 is

5.4 x 10^{6}

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

**Problem 3 : **

Write the given number in scientific notation.

71 x 10^{2}

**Solution :**

Here we don't find decimal point in 71x 10^{2}. So we have to assume that there is decimal point at the end of 71

Then,

71 x 10^{2} ---------> 71. x 10^{2}

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 the decimal point is 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 10^{2} = 7.1 x 10^{1} x 10^{2}

71. x 10^{2} = 7.1 x 10^{3}

Hence, the scientific notation of 71 x 10^{2} is

7.1 x 10^{3}

**Problem 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,

33 x 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 the decimal point is 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 10^{1} x 10^{-3}

33. x 10^{-3} = 3.3 x 10^{-2}

Hence, the scientific notation of 33 x 10^{-3} is

3.3 x 10^{-2}

**Problem 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 the decimal point up to the first non zero digit is 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, the scientific notation of 0.63 x 10^{-3} is

6.3 x 10^{-4}

**Problem 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 the decimal point up to the first non zero digit is 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, the scientific notation of 0.000216 is

2.16 x 10^{-4}

**Problem 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 the decimal point up to the first non zero digit is 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, the scientific notation of 0.0000009 is

9 x 10^{-7}

**Problem 8 :**

Write the given number in scientific notation.

804 x 10^{2}

**Solution :**

Here we don't find decimal point in 804 x 10^{2}. So we have to assume that there is decimal point at the end .

Then,

804 x 10^{2} ---------> 804. x 10^{2}

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 the decimal point is 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 10^{2} = 8.04 x 10^{2} x 10^{2}

804. x 10^{2} = 8.04 x 10^{4}

Hence, the scientific notation of 804 x 10^{2} is

8.04 x 10^{4}

**Problem 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 10^{0}

Hence, the scientific notation of 4.8 is

4.8 x 10^{0}

**Problem 10 :**

Write the given number in scientific notation.

0.99 x 10^{1}

**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 the decimal point up to the first non zero digit is 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 10^{1} = 9.9 x 10^{-1} x 10^{1}

0.99 x 10^{-1} = 9.9 x 10^{0}

Hence, the scientific notation of 0.99 x 10^{-1} is

9.9 x 10^{0}

After having gone through the stuff given above, we hope that the students would have understood, how to write a number in scientific notation.

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