Presentation on theme: "The mass of the Earth is… kg"— Presentation transcript:
1 Scientific notation Express vary large or very small numbers in shorter form
2 The mass of the Earth is… 5980000000000000000000000 kg You could also write 5.98 x 10²⁴ kg
3 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.
4 With scientific notation it is more easily expressed as…. It is inconvenient to express the mass of a proton as a pure decimal.....kgWith scientific notation it is more easily expressed as….x 10⁻²⁷kg
5 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.
6 Write each of the following in scientific notation kgmm³
7 Write each of the following in scientific notation 3,109,000,000 kg x 10m x 10⁻⁵139,044,902 m³ x 10⁸
8 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 x 10⁶ = If it is a negative exponent, move it to the left because it is a small number 3.54 x 10⁻⁶ =
9 Write each of these quantities as a decimal x 10⁷x 10⁻¹²5.67 x 10⁴
10 Write each of these quantities as a decimal x 10⁷ m 80,500,000x 10⁻¹²5.67 x 10⁴ 56,700
11 When multiplying numbers in scientific notation…… Multiply the decimals normallyAdd the exponents of 103.0 x 10⁵ · 3.0 x 10⁵ = 9.0 x 10¹⁰
12 When dividing numbers in scientific notation…… Divide the decimals normallySubtract the denominator’s exponent of 10 from the numerator’s exponent9.0 x 10⁵= x 10²3.0 x 10³
13 When adding or subtracting numbers in scientific notation…. 2 When adding or subtracting numbers in scientific notation… x 10⁵ x 10³ Both numbers must first have the same exponent of x 10³ x 10³= Then you subtract or add the decimals normally and keep the exponent of 10 the same x 10³ or x 10⁵
14 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
15 Perform the following operations 3 x 10 ⁸ X 2 x 10 ⁻²² =8 x 10³ / 2 x 10 ⁸ =1 x 10⁴ x 10² =