**Scientific Notation Worksheet :**

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

Before look at the worksheet, if you would like to learn 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

**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.

Number 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

6.0 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.

Number of digits between the first 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.

Number of digits between the first 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

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.

Number of digits between the first 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.

Number 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.

Number 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.

Number 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.

Number of digits between the first 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

**Solution : **

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

We have to move the decimal to the right.

Number 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^{-1+}^{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.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**