Concept Tutoring - Significant Digits

SIGNIFICANT DIGITS

All non-zero digits are significant digits
Number	Number of Significant Digits
3	1
2.6	2
6263.48	6


Zeroes between non-zero digits are significant digits
Number	Number of Significant Digits
208	3
6.007	4
80.002	5


Zeros to the left of the first non-zero digit (leading zeros) are not significant
Number	Number of Significant Digits
0.0072	2
0.0405	3
0.00000004730	4


Trailing zeros in a decimal number are significant
Number	Number of Significant Digits
0.0020	2
0.00200	3
7.30	3
0.004800	4
0.00372300	6



Trailing zeros in a non-decimal number is ambiguous
Number	Number of Significant Digits
28000	3
28000	4
4000000	2
300.	3


Every digits in a scientific notation are significant
Number	Number of Significant Digits
7x10⁴	1
8.2x10³	2
8.20x10³	3
8.200x10³	4
6.7381 x 10⁴	5
3.2×10⁻⁴	2
3.20×10⁻⁴	3

ARITHMETIC IN SIGNIFICANT DIGITS:

When you multiply or divide numbers, the answer will be the same number of significant digits as the number with the least number of significant digits.

Example:

24.79 x 2.53 = 62.7187
24.79: has 4 significant digits
2.53: has 3 significant digits
62.7187 has 6 significant digits

The result: 62.7 has the least number of significant digits (3 significant digits)

When you add or subtract numbers, the result will have the same number of decimal places as the number with the fewest decimal places.

103.280 + 9.4 – 52.9872 = 59.6928
103.280 has 3 decimal places
9.4 has 2decimal places
52.9872 has 4 decimal places

The result: 52.4 has fewest 2 decimal places