And how they make life easier! Exponents And how they make life easier!

Exponents Exponents are used to write numbers in scientific notation. Exponents are powers of ten. 10 x 10 = 102 = 100 Exponents make math easier. You only work with small numbers. Exponents only show significant figures.

Exponents Some numbers are too long to write. 602 000 000 000 000 000 000 000 or 6.02 x 1023 The exponent tells you how many places the decimal point moved from when the number was written as a decimal or whole number.

Exponents 10-4 = 0.0001 10-3 = 0.001 10-2 = 0.01 10-1 = 0.1 100 = 1 101 = 10 102 = 100 103 = 1000 104 = 10 000

Exponents When you write numbers in scientific notation, the number has two parts. The first part is the mantissa. The mantissa is a number > or = 1 and <10. 1.00 or 9.998 or 5.67 The second part is the 10 and its exponent. 104 or 10-3 or 1034 Write the following in scientific notation

Exponents 347 043.82 72800 72800. 0.0005 0.00060 3.47 x 102 4.382 x 101 7.28 x 104 7.2800 x 104 5 x 10-4 6.0 x 10-4 Doing math with numbers written in scientific notation is a breeze!

Exponents When multiplying numbers written in scientific notation, multiply the mantissas then add the exponents. You may need to adjust the final result so you have a correct mantissa. (6.0 x 102) (7.0 x 103) = 42 x 105 = 4.2 x 106 When dividing, you follow the same steps but subtract the exponents. (6.0 x 102)/(3.0 x 103) = 2.0 x 10-1 {600 divided by 3000 = 0.2 or 2.0 x 10-1}

Exponents When adding or subtracting numbers written in scientific notation, the exponents must agree. (6.0 x 102) + (7.0 x 103) = (0.6 x 103) + (7.0 x 103) = 7.6 x 103 {600 + 7000 = 7600 or 7.6 x 103}

Exponents Try these calculations (7.23 x 10-2) x (6.4895 x 102) = 4.69 x 101 (5.21 x 103) + (7.8 x 102) = 6.0 x 103 (4.557 x 10-1) / (6.22 x 101) = 7.33 x 10-3 (8.10 x 104) – (9.02 x 10-4) = 8.10 x 104