SIG FIG RULES
______ numbers are ALWAYS significant ?
Nonzero
Reason: Nonzero are always the numbers that are significant. Example: 38594.4 = 6 sig fig
In _________________the result should have the same number of decimal places.
Addition and subtraction
Reason: While rounding sig fig and using addition and subtraction you have to make sure your answer has same number of decimal places as the number with the least number of decimal places in your problem.
0.078082= ________ sig figs
5 sig figs
Reasons: The zeros before the decimal doesn't count and the zero after the decimal doesn't count. But everything else after the zeros count as sig figs.
In scientific notation, a number is written as the product of two number: ___________________
A coefficient and 10 raised to a power.
Reason: When you are solving scientific notation you have to make sure that the number is written as the product of two numbers and they have to be a coefficient and 10 raised to a power.
Example: 4.5 x 103
.00012 = ________
1.2 x 10-4
Reason: You move the decimal back to the right 4 places so it makes the exponent negative. When you move it back 4 places your decimal ends up in-between the 1 and the 2 so it become 1.2.
Zeros in front of nonzero digits ( _______________) are not significant.
Leading zeros
Reason: Zeros are not significant
Example: 0.00602 = 3 sig fig ( 602 are the only numbers that count )
In___________________, the result should have the same number of sig figs as the number with the least number of sig figs in the problem.
Multiplication and Division
Reason: While rounding sig figs, when using multiplication and division you have to make sure that your number of sig fig matches the number with the least amount of sig fig in the problem.
770 = ______ sig figs
2 sig figs
Reason:The two sevens at the beginning of the number count as 2 sig figs. The zero at the end doesn't count because its not in-between two nonzero. So that means it doesn't count as a sig fig.
.000 0007 = _______
7.0 x 10-7
Reason: You move the decimal up to the right so it makes the exponent negative.
4.9 x 102 = _________
4.90
Reason: You are moving the decimal up 2 places to the left. So it makes the exponent positive and move the decimal in- between the 4 and the 9.
__________ are all the digits of a measurement that are known with certainty plus one uncertain digit
- Significant Figures
Reason: Significant Figures are all numbers with the decimal making one number uncertain.
7.0000 x 0.003 = __________
.02
Reason: When you are multiplying and dividing sig figs you have to make sure your answer has the same number of sig fig as the number that has the least about of sig figs.
0.00000850 = ____________ sig fig
3 sig figs
Reason: The zero in front of the decimal doesn't count neither does the zeros after the decimal. But the nonzero after the zeros do count ( so the 850 ). The last zero only counts because it is with the 5.
The number 4,500 written in scientific notation is ____________
4.5 x 103
Reason: The power of 10 or exponent the question is 3. The exponent indicates how many times the coefficient must be multiplied by 10 to equal the original number of 4,500.
7.10 x 100 = __________
7.10
Reason: Being that you have no exponents you don't have to move and thing it stays the same.
Zeros_______________ nonzero digits are significant.
Between
Reason: The zeros that are between a nonzero digits become significant.
Example: 50503=5 sig figs ( the zeros between the 5's count as a sig fig )
27.3 x 4.5 = _____
120
Reason: You look at the number with the lowest amount of sig figs. In this equation it is 4.5
74171.7 = _________ sig figs
6 sig figs
Reason: There are no zeros in this problem they are all nonzero. So they all the numbers are significant.
If a number greater than 10, the exponent will be _____________ and is equal to the number of places the decimal must be moved to the ________ to write in scientific notation.
-Positive
- Left
Reason: Any number that is greater than 10 the exponent will be positive and you have move the decimal to the left for your number to be in scientific notation.
8.2 x 10-5 = ___________
.0000082
Reason: Being that the exponent is a -5 it makes this number have 5 zeros in the front of the 82.
Zeros are not significant at the end of a number __________________
Unless there is a decimal
Reason: You only can count the zeros that have decimals the go with it.
Example: 4000 = 1 sig fig
4000.0 = 5 sig figs
0.006 + 0.04 = ________
.05
Reason: You are looking for the number with the least amount of decimal places. Then round to the correct sig fig.
87200 = _________ sig fig
3 sig figs
Reason: It's 3 sig figs because only the first 3 nonzero count when figuring this problem. The two zeros are not significant so they do not count.
If a number is less than 10, the exponent will be __________ and is equal to the number of places the decimal must be moved to the ________ to write the number in scientific notation.
- Negative
- Right
Reason: Any number that is less than 10 the exponent will be negative and you have move the decimal to the right for your number to be in scientific notation.
8 = ____
8 x 100
Reason: The exponent is zero which means the decimal does not move.