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| 16 Theory slides |
| 10 Exercises - Grade E - A |
| Each lesson is meant to take 1-2 classroom sessions |
Here are a few recommended readings before getting started with this lesson.
Decimal Form | Written as a Product or Division Expression | Scientific Notation |
---|---|---|
4505 | 4.505×1000 | 4.505×103 |
8320000 | 8.32×1000000 | 8.32×106 |
0.0005 | 5÷10000 | 5×10-4 |
0.0521 | 5.21÷100 | 5.21×10-2 |
move. Consider a number greater than 10. The decimal would move from right to left to make the number less than 10 but still greater than 1. The number of places the decimal moved indicates the positive exponent to be used for the base 10 power.
Ramsha and her friends did a research project about the highest mountains in the world. They found that Mount Everest is the world's highest mountain. It is located in the Himalayan mountain range. They also learned that Mount Elbrus is the highest peak of Europe. It is in southwestern Russia.
Ramsha and her friends continue to enjoy their school studies. Next is biology class! They use a microscope to examine two types of bacteria, Escherichia coli and Salmonella.
Rewrite the given expression in standard form if it is given in scientific notation. Or rewrite it in scientific notation if it is given in standard form.
Population | Rounded | |
---|---|---|
USA | 331002651 | 300000000 |
Brazil | 212559417 | 200000000 |
Turkey | 84339067 | 80000000 |
China | 1439323776 | 1000000000 |
Australia | 25499884 | 30000000 |
Population | Rounded | Scientific Notation | |
---|---|---|---|
USA | 331002651 | 300000000 | 3×108 |
Brazil | 212559417 | 200000000 | 2×108 |
Turkey | 84339067 | 80000000 | 8×107 |
China | 1439323776 | 1000000000 | 1×109 |
Australia | 25499884 | 30000000 | 3×107 |
Country | Population |
---|---|
USA | 3×108 |
Brazil | 2×108 |
Turkey | 8×107 |
China | 1×109 |
Australia | 3×107 |
Numbers written in scientific notation can be multiplied by using the properties of exponents. Two numbers written in scientific notation a×10b and c×10d can be multiplied by using the Commutative Property of Multiplication and the Product of Powers Property.
(a×10b)×(c×10d)=ac×10b+d
Remove parentheses
Commutative Property of Multiplication
Multiply
The result is 1.8×108. The first factor is greater than 1 and less than 10. The second factor is written as a power of 10. Therefore, the result is already in scientific notation.
Numbers written in scientific notation can be divided by using the properties of exponents. Use the Quotient of Powers Property to divide numbers written in scientific notation.
c×10da×10b=ca×10b−d
Write as a product of fractions
Calculate quotient
Ramsha's math teacher introduced how to multiply and divide numbers written in scientific notation. She then asked the class to work on the following examples.
Remove parentheses
Commutative Property of Multiplication
Multiply
am⋅an=am+n
Write as a product of fractions
Calculate quotient
anam=am−n
Ramsha loves reading science magazines. An article she read said that garden snails move at an incredibly slow speed of only 0.048 kilometers per hour!
Commutative Property of Multiplication
Multiply
am⋅an=am+n
Write as a fraction
Use a calculator
Round to 3 decimal place(s)
anam=am−n
a−(-b)=a+b
Add terms
Perform the following operation and write the result in scientific notation. If necessary, round the first factor of the result to one decimal.
Numbers written in scientific notation can be added or subtracted by adding or subtracting the first factors if the powers of 10 are the same.
(a×10b)±(c×10b)=(a±c)×10b
Ramsha's class took a field trip to learn about wind turbines. The turbines supply lots of households with electricity. A typical large wind turbine can produce 6×106 kilowatt-hour energy per year. A small wind turbine can produce 1.3×105 kilowatt-hour energy per year.
Perform the following operation and write the result in scientific notation. If necessary, round the first factor of the result to one decimal.
Yes, by using scientific notation.
We want to find the value of n in the given equation. 2.8 * 10^(15)=(4* 10^8)(7*10^n) To do it, let's simplify the multiplication on the right-hand side. Then, we will compare it to the left-hand side of the given equation.
Notice that 28 is not less than 10. Therefore, we will rewrite 28 as 2.8 * 10 to rewrite this expression in scientific notation.
We found that the right-hand side of the given equation simplifies to 2.8 * 10^(9+n). Now we can compare the left-hand side with the right-hand side. 2.8 * 10^(15) = 2.8 * 10^(9+n) The first factors are equal to each other. We want to have the same expressions on both sides of the equation. Setting the exponents equal to each other will accomplish that. 15=9+n ⇔ n = 6 We found that the value of n in the given equation is 6.
We will check if the exponent on the left side of the equation is equal to the sum of the exponents on the right side. In Part A, we found that the value of n is 6. Let's substitute it into the equation. 2.8 * 10^(15) = (4 * 10^8)(7 * 10^6) The exponent on the left-hand side is 15. However, the sum of the exponents on the right-hand side of the equation is 14. 8 + 6 = 14 The exponent on the left side is not equal to the sum of the exponents on the right side. Consider the previous part of the exercise. We needed to rewrite the obtained first factor value 28 as 2.8 * 10 to rewrite it in scientific notation. That caused us to change the value of the exponent from 8+n to 9+n.