Notes on Scientific Notation | Grade 8 > Compulsory Maths > Real Number System | KULLABS.COM

Notes, Exercises, Videos, Tests and Things to Remember on Scientific Notation

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• Note
• Things to remember
• Exercise
• Quiz Scientific Notation is used to handle very large or very small numbers. Scientists have developed a shorter method to express very large numbers. It is written as the product of a number (integer and decimal) and a power of 10.

Here are some examples of scientific notation.

 10,000 = 1$$\times$$104 34,567 = 3.4567$$\times$$ 104 1000 = 1$$\times$$103 495 = 4.95 $$\times$$102 10 = 1$$\times$$101 98 = 9.8 $$\times$$101(not usually done) $$\frac{1}{10}$$=1$$\times$$10-1 0.23 = 2.3 $$\times$$10-1(not usually done) $$\frac{1}{100}$$= 1$$\times$$10-2 0.026 = 2.6$$\times$$10-2 $$\frac{1}{1000}$$ = 1$$\times$$10-3 0.0064 =6.4$$\times$$10-3 $$\frac{1}{10,000}$$ = 1$$\times$$10-4 0.00088 = 8.8$$\times$$10-4

Example:

0.000457

= $$\frac{0.000457\times 1000000}{1000000}$$

=$$\frac{457}{10^6}$$

=457$$\times$$ 10-6

=4.57$$\times$$102$$\times$$10-6

= 4.57$$\times$$10-4

• Scientific notation is the way that scientists easily handle very large numbers or very small numbers.
• Scientific notation can be used to turn 0.0000053 into 5.3 x 10-6
• A power of ten with  a positive exponent, such as 105, means the decimal was moved to the left.
• A power of ten with a negative exponent, such as 10-5, means decimal was moved to the right.
.

#### Click on the questions below to reveal the answers

Solution:

324000000

= 324 × 106

= 3.24 × 102× 106

= 3.24 × 102+6

= 3.24 × 108

Solution:

45000000

= 45×106

= 4.5×101×106

= 4.5×101+6

= 4.5×107

Solution:

45

= 4.5×10

= 4.5×101

Solution:

101000

=1.01×100000

=1.01×105

Solution:

0.00671

= $$\frac{6.71}{100000}$$

= $$\frac{6.71×100}{10^5}$$

= 6.71×102-5

=6.71×10-3

Solution:

0.0000435

= $$\frac{0.0000435×10000000}{10000000}$$

= $$\frac{435}{10^7}$$

Solution:

0.0000435

= $$\frac{0.0000435×10000000}{10000000}$$

= $$\frac{435}{10^7}$$

Solution:

= 2.4×105

= 240000

Solution:

= 3.2×104+2.3×104

= (3.2+2.3)×104

= 5.5×104

Solution:

299792458

= 2.99792458 × 100000000

= 2.99792458 × 108 m/s

Solution:

3.2 × 104 + 2.3 × 104

= ( 3.2 + 2.3 )× 104

= 5.5× 104

0%

2.5×103
3.4×103
1.3×103
3.4×93

4.3×10-2
2.3×10-4
2.1×10-5
2.3×10-5

1×10-2
1×9-2
2×10-2
4×10-2

7×106
6×106
2×104
8×106

3.3×10-3
2.7×10-5
4.7×10-1
3.7×10-5

22000
10000
22500
23000

3.45678×102
3.44677×103
3.45678×103
3.45677×103

8.72×10-5
5.11×10-5
7.71×10-5
6.71×9-5
• ### The mass of the moon is 73,000,000,000,000,000,000,000 kg. What is this written in scientific notation.

7.2( imes) 1019 kg
7.2( imes)1018 kg
7.2( imes)1017 kg
7.2( imes)1015kg
• ### Simplify:(4( imes)105) ( imes)(3( imes)106)

1.2( imes)1015
1.2( imes)1011
1.2( imes)1010
1.2( imes)1012
• ### Simplify:(7( imes)108)( imes)(2( imes)1010)

1.4( imes)1010
1.4( imes)1012
1.4( imes)1015
1.4( imes)1019
• ### Simplify the following and give your answers in scientific notation:108+ 106

1.01( imes)1012
1.01( imes)1015
1.01( imes)1010
1.01( imes)108

24,0000
2400000
24000
2400
• ### Write 7.085( imes)10-14 as an ordinary number.

0.00000000007085
0.0000000000000085
0.00000000007085
0.00000000000007085
• ### Simplify:4.5( imes)107- 2.2( imes)106

4.289 imes)1012
4.28( imes)107
4.28( imes)109
4.28( imes)108