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Magnitude Order of Operations 8.EE.3 Use number expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is that the other. 8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Students write, add and subtract numbers in scientific notation and understand what is meant by the term leading digit. WKSP HW Procedure Media Student Outcomes Standard Pre Requisite Scientific Notation #17 Spiral #4 Foldable Concentration ‘I have, who has …’ Scientific Notation The estimated number of stars in the universe is 6 x 1022. What is this number in standard form? 1 < d < 10 d x 10n Complete the following by indicating the order of magnitude: 234.567 = 234.567 x 10 = 23.4567 x 10 = 2.34567 x 10 = 0.234567 x 10 = 2345.67 x 10 = 23456.7 x 10 = 234567 x 10 Only one of the expressions above is in scientific notation. Which one? Exercise: State whether the following numbers are written in scientific notation. If not, state the reason. 1. 1.908 x 1017 ̅̅̅̅ + 107 2. 4.0701 3. 0.325x 10-2 4. 18.432 x 58 Scientific Notation Operations We can apply all four operations (+, -, x, ÷) to numbers in scientific notation! When adding (or subtracting), each number must be in the _____ order of magnitude. Example: We want to find the difference in the populations of Texas and North Dakota. In 2012, Texas had a population of about 26 million people and North Dakota had a population of about 6.9 x 104. Texas = 26,000,000 = 2.6 x 10 North Dakota = 6.9 x 104 Example: We want to find the combined mass of two hydrogen atoms and one oxygen atom (H2O). A hydrogen atom weighs 1.7 x 10-27 kg and an oxygen atom weighs 2.7 x 10-26 kg. Example: All planets revolve around the sun in elliptical orbits. Uranus’s furthest distance from the sun is approximately 3.004 x 109 km, and its closest distance is approximately 2.749 x 109 km. Using this information, what is the average distance of Uranus from the sun? Scientific Notation Name: __________________________________ Pre-Algebra Date: ______ Exit Ticket approximate total surface area of Earth is 5.1 × 108 𝑘𝑚2 . Salt water has an approximate surface area of 352,000,000 𝑘𝑚2 and freshwater has an approximate surface area of 9 × 106 𝑘𝑚2. How much of Earth’s surface is covered by water, including both salt and fresh water? Write your answer in scientific notation. 1. The 2. How much of Earth’s surface is covered by land? Write your answer in scientific notation. 3. Approximately how many times greater is the amount of Earth’s surface that is covered by water, compared to the amount of Earth’s surface that is covered by land? Scientific Notation Name: _______________________________________ Pre-Algebra Date: _____ HW #17 1. Write the number 68,127,000,000,000,000 in scientific notation. 2. There are approximately 7.5 x 1018 grains of sand on Earth. There are approximately 7 x 1027 atoms in an average human body. Are there more grains of sand on Earth or atoms in an average human body? About how many times more atoms are in a human body, compared to grains of sand on Earth? 3. The speed of light is 300,000,000 meters per second. The sun is approximately 1.5 x 1011 meters from Earth. How many seconds does it take for sunlight to reach Earth? Review: 4. The Formax Dwarf galaxy is 4.6 x 105 light-years away from Earth, while Andromeda I is 2.430 x 106 light-years away from Earth. Which is closer to Earth? 1 5. Simplify: (2 ) × (−8) 4