Rounding and percent error
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1) To estimate quickly, round numbers to values that allow for mental math, do the calculation with simplified numbers, and check if the estimate seems reasonable. 2) Percentage error compares the difference between an estimate and actual value relative to the actual value, with a smaller percentage error indicating a more accurate estimate. 3) Standard form (scientific notation) expresses very small or large numbers as a coefficient between 1 and 10 multiplied by a power of 10, such as 1.23x103 for 1,230 or 3.47x10-2 for 0.0347.
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Scientific notation is a way to write very large or small numbers in their simplest form. It involves writing a number as the product of a coefficient and a power of 10. To divide numbers in scientific notation, you divide the coefficients, subtract the exponents, shift the decimal if needed to keep the coefficient between 1 and 10, and write the result with the new exponent. Some examples of dividing numbers in scientific notation are worked out step-by-step. The document also provides practice problems for dividing numbers in scientific notation and examples of using scientific notation to solve real-world problems involving distances and speeds.
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This document discusses various concepts related to measurement and errors in measurement. It defines physical quantities, units of measurement, and the classification of quantities into fundamental and derived quantities. It also explains the International System of Units (SI units), prefixes used with SI units, and rules for writing SI units. The document discusses the concepts of significant figures and counting significant figures in measurements. It describes different types of errors in measurement such as systematic errors, gross errors, and random errors. It also explains the concepts of absolute error, mean absolute error, relative error, percentage error, and least count error. Finally, it discusses the combination of errors in different mathematical operations.
Chem 101 week 2
This document provides an overview of significant figures and measurement in chemistry. It defines significant figures and digits, and discusses rules for determining significant figures in measurements and calculations. It also summarizes the metric system of units, focusing on units of length, mass, volume, and temperature. Key topics covered include conversion between units using dimensional analysis and conversion factors.
Motivation
Decimals are commonly used in measurements and commerce. They allow numbers to be represented on the number line through repeated subdivision into tenths. A decimal number locates a point on the number line through the place value of its digits. Decimals extend the place value concept for whole numbers to include tenths, hundredths, thousandths, and so on. While widely used today, decimals were not commonly adopted until the early 17th century. Decimals can represent both rational and some irrational numbers and are useful for approximations and measurements recorded to a given accuracy.
PowerPointCh2_Section2.4.pdf
This document discusses rules for rounding numbers and calculations to the appropriate number of significant figures. It explains that in multiplication and division, the final answer should have the same number of significant figures as the term with the fewest significant figures. For addition and subtraction, the answer should have the same number of decimal places as the term with the fewest decimal places. When multiple operations are involved, rounding should occur only after all calculations are complete. Examples are provided to illustrate the various rules.
NCV 3 Mathematical Literacy Hands-On Support Slide Show - Module 3
This slide show complements the learner guide NCV 3 Mathematical Literacy Hands-On Training by San Viljoen, published by Future Managers. For more information visit our website www.futuremanagers.net
Chapter 02
- The document discusses counting and rounding significant figures when performing calculations with measurements. It provides rules for determining the number of significant figures in products, quotients, sums, and differences.
- It also discusses common units in the International System of Units (SI) including prefixes, and provides examples of unit conversions using dimensional analysis and setting up conversion factors.
Scientificnotation
Scientific notation is a way to write very large or small numbers in a more compact form. To write a number in scientific notation, you express it as the product of two factors: a decimal number greater than or equal to 1 but less than 10, and a power of 10. For example, 93,000,000 would be written as 9.3 x 107. The power of 10 indicates how many places the decimal is moved. Very small decimals between 0 and 1 use a negative power of 10. For example, 0.00064 would be written as 6.4 x 10-4. Scientific notation makes large and small numbers easier to work with
Fishlock Lesson One Standard Form
The document discusses standard form (also called scientific notation), which is a way of writing numbers that are very large or very small using exponents of 10. It provides examples of writing numbers like the mass of the Earth in standard form and explains how to perform calculations like multiplication and division when numbers are in standard form. Key rules covered include keeping the number between 1 and 10 when writing in standard form and combining the exponents when multiplying or dividing numbers in standard form.
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Rounding and percent error
- 1. Important considerations for rounding: Rounding during a calculation can lead to a less accurate result, you need to decide how accurate you need the answer to be in order to decide if it is acceptable to round during a calculation.
- 2. To estimate quickly: 1. Round the numbers to values that you can do mental math with 2. Do the calculation with the simplified numbers 3. Think about whether your estimate seems to big or too small
- 3. Do in class: page 19 Exercises 1.5 #’s 1 - 4
- 4. Percentage Error – works out the difference between the estimate and the actual value in relation to the size of the actual value. * the smaller the percentage error the more accurate the estimate Calculating percentage error: VE = exact value VA = approximate amount
- 5. Do : Exercises 1.6 #’s 1 & 2 page 21
- 6. Standard Form (Scientific Form) - a way to express very small or very large numbers Form: a x 10n where a 1 ≤ a < 10 Example: 1,230 in standard form is 1.23 x 103 Example: 0.0347 in standard form is 3.47 x 10-2
- 7. Transforming large numbers: 1. First write down the number and place a decimal point where the number will be between 1 and 10 2. Count the number of places the decimal has moved 3. Number of places moved is the positive power of 10 Example: 1) 3,254,000 3.254 2) then count the number of places the decimal moved, in this case 6 places. 3) The standard form is 3.254 x 106
- 8. Transforming small numbers to standard form: 1. Place the decimal so the number is between 1 and 10 2. Count the number of decimal places moved 3. The number of decimal places moved is the negative power of 10 Example: 1. 0.00056 5.6 2. Count number of decimal places moved, in this case 4 3. The standard form is 5.6 x 10-4
- 9. Thursday: Quiz on Real numbers, Rounding, and Significant digits