6.0.0. SMALLER NUMBERS AND LARGER NUMBERS:
In physics, we deal with smaller numbers and larger numbers. It is there superlative that you get a good understanding of smaller numbers and larger numbers.
SMALL NUMBERS:
Small numbers are numbers that are less than one. Prefixes are attached to the base words to indicate the value of the numbers.
Number. Standard form Name Prefix. Symbol
0.1 10 ¯ ¹ m decimeter deci d
0.01 10 ¯ ² m centimeter Centi c
0.001 10 ¯ ³ m millimeter milli m
0.000001 10 ¯ ⁶ m micrometer micro ?
LARGE NUMBERS:
Number. Standard Form. Name. Prefix. Symbol
10. 10 ¹ m. Decametre. Deca. D
100. 10 ² m. Hectometer. Hecto. h
1000. 10 ³ m. Kilometer. Kilo. K
1000000. 10 ⁶ m mega meter. Mega. M
NUMBERS IN STANDARD FORM
Numbers in standard form are written in the general form of A x 10¯ᵇ
Where A represent a negative or positive number from zero and above while b is the power to which 10 is raised. b can be negative or positive.
Examples of Numbers in Standard Form:
i ) 2 x 10 ¯ ³. (ii) 4.12 x 10 ⁵ (iii) 12.54 x 10¯⁴. (iv) 200 x 10 and so on.
NUMBERS IN ORDINARY FORM:
Our usual way or writing numbers are the ordinary forms of numbers.
Examples are: 1.234, 4.5426 , 0.2903 , 0.005426, 23478, 10000, etc are numbers in their ordinary forms.
Changing Numbers in standard Form to Ordinary Form:
2.5 x 10¯ ⁵ = 2.5 x 10 x 10 x 10 x 10 x 10. = 2.5 x 100000. = 250000
0.0123 x 10¯ ⁷ = (123÷10000) x 10 x 10 x 10 x 10 x 10 x 10 x 10
= (123÷10000) x 10000000 = 123000
5.23 x 10¯ ⁵ = 5.23 x (1 ÷ 10¯ ⁵ ) = 5.23 x (1 ÷ 100000) = 5.23 ÷ 100000
= 0.0000523¯ ¹⁰
EXERCISE:
Change the following numbers in standard form to their ordinary forms:
i12.54 x 10 ³. 0.0234 x 10⁶ 0.54 x 10⁹ 542.7 x 10⁵
3.23 x 10^~5. 63.43 x 10 ¯ ⁶. 546 x 10¯ ⁹ . 0.45 x 10¯¹²
Change the following numbers to standard form:
0.00564. 234576. 2.345. 0.6573. 124357. 20045
In physics, we deal with smaller numbers and larger numbers. It is there superlative that you get a good understanding of smaller numbers and larger numbers.
SMALL NUMBERS:
Small numbers are numbers that are less than one. Prefixes are attached to the base words to indicate the value of the numbers.
Number. Standard form Name Prefix. Symbol
0.1 10 ¯ ¹ m decimeter deci d
0.01 10 ¯ ² m centimeter Centi c
0.001 10 ¯ ³ m millimeter milli m
0.000001 10 ¯ ⁶ m micrometer micro ?
LARGE NUMBERS:
Number. Standard Form. Name. Prefix. Symbol
10. 10 ¹ m. Decametre. Deca. D
100. 10 ² m. Hectometer. Hecto. h
1000. 10 ³ m. Kilometer. Kilo. K
1000000. 10 ⁶ m mega meter. Mega. M
NUMBERS IN STANDARD FORM
Numbers in standard form are written in the general form of A x 10¯ᵇ
Where A represent a negative or positive number from zero and above while b is the power to which 10 is raised. b can be negative or positive.
Examples of Numbers in Standard Form:
i ) 2 x 10 ¯ ³. (ii) 4.12 x 10 ⁵ (iii) 12.54 x 10¯⁴. (iv) 200 x 10 and so on.
NUMBERS IN ORDINARY FORM:
Our usual way or writing numbers are the ordinary forms of numbers.
Examples are: 1.234, 4.5426 , 0.2903 , 0.005426, 23478, 10000, etc are numbers in their ordinary forms.
Changing Numbers in standard Form to Ordinary Form:
2.5 x 10¯ ⁵ = 2.5 x 10 x 10 x 10 x 10 x 10. = 2.5 x 100000. = 250000
0.0123 x 10¯ ⁷ = (123÷10000) x 10 x 10 x 10 x 10 x 10 x 10 x 10
= (123÷10000) x 10000000 = 123000
5.23 x 10¯ ⁵ = 5.23 x (1 ÷ 10¯ ⁵ ) = 5.23 x (1 ÷ 100000) = 5.23 ÷ 100000
= 0.0000523¯ ¹⁰
EXERCISE:
Change the following numbers in standard form to their ordinary forms:
i12.54 x 10 ³. 0.0234 x 10⁶ 0.54 x 10⁹ 542.7 x 10⁵
3.23 x 10^~5. 63.43 x 10 ¯ ⁶. 546 x 10¯ ⁹ . 0.45 x 10¯¹²
Change the following numbers to standard form:
0.00564. 234576. 2.345. 0.6573. 124357. 20045
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