Scientific Notation• Sometimes numbers are too big or too small to write

with ease and clarity– The Andromeda Galaxy (the closest one to our Milky Way

galaxy) contains at least 200,000,000,000 stars. – The weight of an alpha particle, which is emitted in the

radioactive decay of Plutonium-239, is0.000,000,000,000,000,000,000,000,006,645 kilograms.

• Scientific notation is used to express these large or small numbers in a convenient way

• Remember that:– 100 = 10 X 10 = 102

– 1000 = 10 X 10 X 10 = 103

– 10,000 = 10 X 10 X 10 X 10 = 104

ExampleWrite 4,776 in scientific notation

Place the decimal immediately to the right of the left-most non-zero number. This should give you a number between

one and ten.

4.776Count the number of digits between the old and the new

decimal point, this gives the power, n of 10 (10n).

4 776 X 103

Since the decimal is shifted to the left, the exponent is positive.

4.776 x 103

3 Digits

Check for UnderstandingWrite 0.0246 in scientific notation

Place the decimal immediately to the right of the left-most non-zero number. This should give you a number between

one and ten

2.46Count the number of digits between the old and the new

decimal point, this gives the power, n of 10 (10n).

X 10-2

Since the decimal is shifted to the right, the exponent is negative.

2.46 x 10-2

2 Digits

0 02 46

Check for UnderstandingWrite 4.953 x 104 in standard form

Write the decimal number.

4.953Move the decimal the number of places specified by the powers of ten: to the right since it is positive.

X 104 4 9530Rewrite the number in integer/standard form.

49,530

4 Places

Write 8.397 x 10-1 in standard form

Write the decimal number.

8.397Move the decimal the number of places specified by

the powers of ten: to the left since it is negative.

X 10-1 0 8 397Rewrite the number in integer/standard form.

0.8397

1 Place

Multiplying and Dividing With Your Calculator

1. Punch the number (the digit number) into your calculator.

2. Push the EE or EXP button. Do NOT use the x (times) button!!

3. Enter the exponent number. Use the +/- button to change its sign.

4. Voila! Treat this number normally in all subsequent calculations.

Check for Understanding

• You can use scientific notation to complete calculations without a calculator for ridiculously huge numbers

• Example• Multiply 2,500,000,000,000,000 times

4,000,000,000Answer?

Check for Understanding

• You can use scientific notation to complete calculations without a calculator for ridiculously huge numbers

• Example• Multiply 2,500,000,000,000,000 times

4,000,000,000Answer? 1 X 1025