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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!