Scientific notation

Express vary large or very small numbers in shorter form

The mass of the Earth is…

5980000000000000000000000 kg

You could also write 5.98 x 10²⁴ kg

To write a very large number in scientific notation…

move the decimal to the left so it is after the first digit

the number of spaces you move the decimal to the left becomes

the exponent over your 10.

It is inconvenient to express the mass of a proton as a pure decimal.....

.00000000000000000000000000167262 kg

With scientific notation it is more easily expressed as….

1.67262 x 10⁻²⁷kg

• To write a very small number in scientific notation…

….move the decimal to the right so it is after the first digit

the number of spaces you move the decimal to the right becomes the negative exponent over your 10.

Write each of the following in scientific notation

• 31090000000000000 kg

• .0000345 m

• 139044902345 m³

Write each of the following in scientific notation

• 3,109,000,000 kg 3.109 x 10

• .0000345 m 3.45 x 10⁻⁵

• 139,044,902 m³ 1.39044902 x 10⁸

To convert a number from scientific notation into a decimal remember:

Move the decimal the number of spaces equal to the exponent over ten.

If it is a positive exponent, move it to the right to make it a large number.

3.54 x 10⁶ = 354000.If it is a negative exponent, move it to the left

because it is a small number3.54 x 10⁻⁶ = .00000354

Write each of these quantities as a decimal

8.05 x 10⁷

4.9000 x 10⁻¹²

5.67 x 10⁴

Write each of these quantities as a decimal

8.05 x 10⁷ m 80,500,000

4.9000 x 10⁻¹².0000000000049000

5.67 x 10⁴ 56,700

When multiplying numbers in scientific notation……

• Multiply the decimals normally• Add the exponents of 10

3.0 x 10⁵ · 3.0 x 10⁵ = 9.0 x 10¹⁰

When dividing numbers in scientific notation……

• Divide the decimals normally• Subtract the denominator’s exponent of 10

from the numerator’s exponent

9.0 x 10⁵------------ = 3.0 x 10²3.0 x 10³

When adding or subtracting numbers in scientific notation…..

2.8 x 10⁵ + 1.5 x 10³

Both numbers must first have the same exponent of 10.

280 x 10³ + 1.5 x 10³=

Then you subtract or add the decimals normally and keep the exponent of 10 the same.

281.5 x 10³ or 2.815 x 10⁵

Of course, most of this will be done on your calculator, but

remember…• You must always put numbers in parentheses

if you type them in scientific notation, or use the trick below.

• Get used to using the 2nd , EE button(3.5 x 10^5)Is the same as3.5 E 5 and no parentheses are required

Perform the following operations

• 3 x 10 ⁸ X 2 x 10 ⁻²² =

• 8 x 10³ / 2 x 10 ⁸ =

• 1 x 10⁴ + 8 x 10² =