Understanding Scientific Notation

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For example, the distance from Earth to the sun can be written as 93 million miles in decimal form, but using scientific notation we can simplify this to 9.3 × 107 miles. This tells us that there are seven digits after the first digit (which is a 9), and so we multiply by 10 to the power of 7. Similarly, if you want to write out the number of atoms in a molecule of water (6.02 × 1023 particles per mole), it would take forever to do that in decimal form. Instead, we use scientific notation: 6.02 × 1023. This tells us that there are 23 digits after the first digit (which is a 6), and so we multiply by 10 to the power of 23. Scientific notation can also be used for very small numbers, like the mass of an electron (9.1 × 10-31 kilograms). In this case, the number of zeros at the start tells us how many digits are missing before we get to our first non-zero digit. So there are 31 digits missing before we get to the 9 and the 1, which means that we multiply by 10 to the power of -31.
To write scientific notation on a calculator, use the button labelled as ×10𝑥 or just 10𝑥. Enter the coefficient (the number between 1 and 10)Then press the ×10𝑥 buttonThen enter the power of 10

Here are some examples:
– To write 35,400 in scientific notation on a calculator with ‘×10𝑥’ button, you would first divide 35,400 by 10, which gives us 3.54 x 10^3 (the exponent is the number of times we multiplied or divided by 10 to get from our original number to a coefficient between 1 and 10).
– To write 0.0002 in scientific notation on a calculator with ‘×10𝑥’ button, you would first move the decimal point four places to the right (which is equivalent to multiplying by 10^4), giving us 2 x 10^-4 (the exponent is negative because we moved the decimal point to the left).
– To write 3.5 x 10^7 on a calculator with ‘×10𝑥’ button, you would first enter 3.5 and then press the ‘×10𝑥’ button (which is usually labeled as ‘E’ or ‘EXP’). Then, enter 7 to set the exponent.
– To write 2 x 10^-6 on a calculator with ‘×10𝑥’ button, you would first enter 2 and then press the ‘×10𝑥’ button (which is usually labeled as ‘E’ or ‘EXP’). Then, enter -6 to set the exponent.
– To write 5 x 10^3 on a calculator with ‘×10𝑥’ button, you would first enter 5 and then press the ‘×10𝑥’ button (which is usually labeled as ‘E’ or ‘EXP’). Then, enter 3 to set the exponent.
– To write 2 x 10^-8 on a calculator with ‘×10𝑥’ button, you would first enter 2 and then press the ‘×10𝑥’ button (which is usually labeled as ‘E’ or ‘EXP’). Then, enter -8 to set the exponent.
– To write 354 x 10^6 on a calculator with ‘×10𝑥’ button, you would first enter 354 and then press the ‘×10𝑥’ button (which is usually labeled as ‘E’ or ‘EXP’). Then, enter 6 to set the exponent.

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