Nt1310 Unit 6 Lab Report
In measuring substances in the lab, reporting data, and performing calculations, it is both crucial important to be as precise and accurate as possible and also not to report false data. The rules of significant figures (digits in a measurement that reflect the measurement’s accuracy) allow us to have a methodical means of ensuring that the data and calculations we report reflect the accuracy that the equipment or data provide. To follow the guidelines for the correct number of significant figures, it is important to know the rules for multiplication and division, for addition and subtraction, for rounding, for measuring, and for scientific notation.
When multiplying or dividing quantities, the number of significant figures in an answer should have should contain the total amount of digits of the least precise piece of …show more content…
provided data or measurement.
For example, when multiplying 150.0 x 8.2453, the calculator will say the answer is 1236.795. However, the least precise piece of data (150.0) has only 4 significant figures, so the answer will reflect that. Therefore, the answer is rounded to 4 significant figures and would be reported as 1236.
When adding or subtracting quantities, the number of significant figures is rounded off to the same decimal place as the least precise piece of data. For example, when subtracting 23.385 cm from 18472.3952 cm, the answer will be rounded to the third decimal place, leaving our answer to be 18449.010 cm. It is important to note that defined quantities, such as the number of people at a table, or minutes in an hour,are not subjected to the rules of significant figures because they would not fall victim to erroneous measurements.
These "exact" numbers can have infinite significant figures, or as many as we would like to use. Simultaneously, it is important that when performing long calculations to only round at the end, when reporting an answer. Rounding many times throughout performing calculations detracts from accuracy. It is also important to note that trailing zeroes in large numbers and leading zeroes in decimals are not significant. For example, 1,000,000 in only has one significant digit, and 0.0034 g only has 2. However, zeroes in between digits are always significant. Meanwhile, in a number such as 150.0 m, the data provided asserts that this information is accurate to 4 significant figures. In the case of 120 yd, however, there is no indication that this data is accurate past 2 significant figures. Sometimes, this could be reported as 120. and one would know that this data is accurate to 3 significant figures. In the case of reporting a large or small number that also has a very limited amount of significant figures, one can put results in scientific notation to make these numbers easier to read. 1,000,000 can become 1 x 106 and .0034 g can become 3.4 x 10-3.
The display of our calculator will typically show more digits that are justified. The rounding procedure is to identify the position of the last digit justified by the significant figure rule being applied,and then to look at the digit to its right. If that digit to the right is 4 or less, leave the last digit to be kept as it is; if the digit to the right is 5 or greater, round the last digit to be kept upward by one increment.
Finally, when taking measurements, it is also important to adhere to the rules of significant figures. Here, you should measure to the most precise value the instrument allows you to measure to, and then estimate the last value.
While these rules may seem annoying at first, it is important to master them in order to ensure that data and calculations reflect the correct accuracy allotted by the equipment used.
When multiplying or dividing quantities, the number of significant figures in an answer should have should contain the total amount of digits of the least precise piece of …show more content…
provided data or measurement.
For example, when multiplying 150.0 x 8.2453, the calculator will say the answer is 1236.795. However, the least precise piece of data (150.0) has only 4 significant figures, so the answer will reflect that. Therefore, the answer is rounded to 4 significant figures and would be reported as 1236.
When adding or subtracting quantities, the number of significant figures is rounded off to the same decimal place as the least precise piece of data. For example, when subtracting 23.385 cm from 18472.3952 cm, the answer will be rounded to the third decimal place, leaving our answer to be 18449.010 cm. It is important to note that defined quantities, such as the number of people at a table, or minutes in an hour,are not subjected to the rules of significant figures because they would not fall victim to erroneous measurements.
These "exact" numbers can have infinite significant figures, or as many as we would like to use. Simultaneously, it is important that when performing long calculations to only round at the end, when reporting an answer. Rounding many times throughout performing calculations detracts from accuracy. It is also important to note that trailing zeroes in large numbers and leading zeroes in decimals are not significant. For example, 1,000,000 in only has one significant digit, and 0.0034 g only has 2. However, zeroes in between digits are always significant. Meanwhile, in a number such as 150.0 m, the data provided asserts that this information is accurate to 4 significant figures. In the case of 120 yd, however, there is no indication that this data is accurate past 2 significant figures. Sometimes, this could be reported as 120. and one would know that this data is accurate to 3 significant figures. In the case of reporting a large or small number that also has a very limited amount of significant figures, one can put results in scientific notation to make these numbers easier to read. 1,000,000 can become 1 x 106 and .0034 g can become 3.4 x 10-3.
The display of our calculator will typically show more digits that are justified. The rounding procedure is to identify the position of the last digit justified by the significant figure rule being applied,and then to look at the digit to its right. If that digit to the right is 4 or less, leave the last digit to be kept as it is; if the digit to the right is 5 or greater, round the last digit to be kept upward by one increment.
Finally, when taking measurements, it is also important to adhere to the rules of significant figures. Here, you should measure to the most precise value the instrument allows you to measure to, and then estimate the last value.
While these rules may seem annoying at first, it is important to master them in order to ensure that data and calculations reflect the correct accuracy allotted by the equipment used.