Rules in identifying significant digits
The rules for identifying significant digits when writing or interpreting numbers are as follows:
All non-zero digits are considered significant. For example, 91 has two significant digits (9 and 1), while 123.45 has five significant digits (1, 2, 3, 4 and 5).
Zeros appearing anywhere between two non-zero digits are significant. Example: 101.12 has five significant digits: 1, 0, 1, 1 and 2.
Leading zeros are not significant. For example, 0.00052 has two significant digits: 5 and 2.
Trailing zeros in a number containing a decimal point are significant. For example, 12.2300 has six significant digits: 1, 2, 2, 3, 0 and 0. The number 0.000122300 still has only six significant digits (the zeros before the 1 are not significant). In addition, 120.00 has five significant digits. This convention clarifies the precision of such numbers; for example, if a result accurate to four decimal places is given as 12.23 then it might be understood that only two decimal places of accuracy are available. Stating the result as 12.2300 makes clear that it is accurate to four decimal places.
The significance of trailing zeros in a number not containing a decimal point can be ambiguous. For example, it may not always be clear if a number like 1300 is accurate to the nearest unit (and just happens coincidentally to be an exact multiple of a hundred) or if it is only shown to the nearest hundred due to rounding or uncertainty. Various conventions exist to address this issue:
A bar may be placed over the last significant digit; any trailing zeros following this are insignificant. For example, has three significant digits (and hence indicates that the number is accurate to the nearest ten).
The last significant digit of a number may be underlined; for example, "20000" has two significant digits.
A decimal point may be placed after the number; for example "100." indicates specifically that three significant digits are meant.
4 Basic Operations
Addition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign (+). For example, in the picture on the right, there are 3 + 2 apples—meaning three apples and two other apples—which is the same as five apples. Therefore, 3 + 2 = 5. Besides counts of fruit, addition can also represent combining other physical and abstract quantities using different kinds of numbers: negative numbers, fractions, irrational numbers, vectors, decimals and more. Addition follows several important patterns. It is commutative, meaning that order does not matter, and it isassociative, meaning that when one adds more than two numbers, order in which addition is performed does not matter. Repeated addition of 1 is the same as counting; addition of 0 does not change a number.
Subtraction is one of the four basic arithmetic operations; it is the inverse of addition, meaning that if we start with any number and add any number and then subtract the same number we added, we return to the number we started with. Subtraction is denoted by a minus sign.
The traditional names for the parts of the formula
c − b = a
Multiplication (symbol "×") is the mathematical operation of scaling one number by another. It is one of the four basic operations. Because the result of scaling by whole numbers can be thought of as consisting of some number of copies of the original, whole-number products greater than 1 can be computed by repeated addition; for example, 3 multiplied by 4 (often said as "3 times 4") can be calculated by adding 4 copies of 3 together:
in mathematics, especially in elementary arithmetic, division (÷) is the arithmetic operation that is the inverse of multiplication.
For instance,
since:
Division is often introduced through the notion of "sharing out" a set of objects, for example a pile of sweets, into a number of equal portions. Distributing the objects several at a time in each round of sharing to each portion leads to the idea of "chunking", i.e. division by repeated subtraction.
Basic Rules on operations
Addition and Subtraction
The computed measurement is rounded off according to the least number of decimal places
Multiplication and Division
The computed measurements must be rounded off according to the least number of significant digits
Rounding is often done on purpose to obtain a value that is easier to write and handle than the original. It may be done also to indicate the accuracy of a computed number; for example, a quantity that was computed as 123,456 but is known to be accurate only to within a few hundred units is better stated as about 123,500.
Example:
Generally, the same rules apply to numbers expressed in scientific notation. However, in the normalized form of that notation, placeholder leading and trailing digits do not occur, so all digits are significant. For example, 0.00012 (two significant digits) becomes 1.2×10−4, and 0.000122300 (six significant digits) becomes 1.22300×10−4. In particular, the potential ambiguity about the significance of trailing zeros is eliminated. For example, 1300 to four significant digits is written as 1.300×103, while 1300 to two significant digits is written as 1.3×103.
Examples:
1. 0.000000002056 = 2.056 x 10-9
2. 89684.25 = 8.968425 x 104
3. 0.00000014325 = 1.4325 x 10-7
Manere
Perez
The computed measurement is rounded off according to the least number of decimal places
Multiplication and Division
The computed measurements must be rounded off according to the least number of significant digits
Rounding off
Rounding a numerical value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example, replacing US$ 23.4476 by US$ 23.45, or the fraction 312/937 by 1/3, or by 1.41.Rounding is often done on purpose to obtain a value that is easier to write and handle than the original. It may be done also to indicate the accuracy of a computed number; for example, a quantity that was computed as 123,456 but is known to be accurate only to within a few hundred units is better stated as about 123,500.
Example:
- 250. 3471 = 250. 348
- 198 = 200
- 178.28 = 180
Scientific Notation
Generally, the same rules apply to numbers expressed in scientific notation. However, in the normalized form of that notation, placeholder leading and trailing digits do not occur, so all digits are significant. For example, 0.00012 (two significant digits) becomes 1.2×10−4, and 0.000122300 (six significant digits) becomes 1.22300×10−4. In particular, the potential ambiguity about the significance of trailing zeros is eliminated. For example, 1300 to four significant digits is written as 1.300×103, while 1300 to two significant digits is written as 1.3×103.
Examples:
1. 0.000000002056 = 2.056 x 10-9
2. 89684.25 = 8.968425 x 104
3. 0.00000014325 = 1.4325 x 10-7
EXERCISES!
Express the following in scientific notation, round off to the nearest 100ths
Given
1) 0.00086425
2) 5355484000
3) 40221100
4) 0.000635
5) 45255890000
Check your answers!
Scientific notation
1) 8.64 x 10-4
2) 5.36 x 109
3) 4.02 x 107
4) 6.35 x 10-4
5) 4.53 x 1010
MEMBERS:
Sison
Castillo
Gonzales, Carissa
Manere
Perez
Sources:
http://en.wikipedia.org/wiki/Subtraction
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