Fox Valley Technical College Appleton WI Telecom Field

Fox Valley Technical College Appleton, WI Telecom Field Service Certificate Communication Signals Expressions Used for Numbers

Writing Down Numbers There are different methods of expressing large and small decimal numbers. Powers of Ten Scientific Notation Engineering Notation Abbreviations

Scientific Notation – Numbers ≥ 1 Multiplier 1, 000, 000 100, 000 10, 000 1, 000 100, 000 1, 000 10 1 = = = = = Power of Ten 1 x 109 1 x 108 1 x 107 1 x 106 1 x 105 1 x 104 1 x 103 1 x 102 1 x 101 1 x 100

Examples Scientific Notation – Numbers ≥ 1 Number Scientific Notation 37, 195 = 3. 7195 x 104 450, 379 = 4. 50379 x 105 98 = 9. 8 x 101 8. 6023 = 8. 6023 (x 100) • Move the decimal point to the left until just one digit remains to the left of it. • Multiply times 10+X where X is the number of places the decimal point was moved to the left.

Scientific Notation – Numbers <1 Multiplier 0. 1 0. 001 0. 00001 0. 0000001 0. 000000001 0. 00000000001 0. 0000001 = = = Power of Ten 1 x 10 -1 1 x 10 -2 1 x 10 -3 1 x 10 -4 1 x 10 -5 1 x 10 -6 1 x 10 -7 1 x 10 -8 1 x 10 -9 1 x 10 -10 1 x 10 -11 1 x 10 -12

Examples Scientific Notation – Numbers <1 Number Scientific Notation 0. 6374 = 6. 374 x 10 -1 0. 00002473 = 2. 473 x 10 -5. 025398 = 2. 5398 x 10 -2 0. 0000000271 = 2. 71 x 10 -8 • Move the decimal point to the right until just one digit remains to the left of it. • Multiply times 10 -X where X is the number of places the decimal point was moved to the right.

Engineering Notation – Numbers ≥ 1 Abbreviation Units Prefix Multiplier Power of 10 T Tera- x 1, 000, 000 x 1012 G Giga- x 1, 000, 000 x 109 M Mega- x 1, 000 x 106 K Kilo- x 1, 000 x 103 Engineers only use powers of ten that are multiples of 3.

Examples Engineering Notation – Numbers ≥ 1 Number Engineering Notation 37, 195 = 37. 195 x 103 or 37. 195 Kilo-units 450, 379 = 450. 379 x 103 or 450. 379 Kilo-units 98. = 98 (x 100) 8. 6023 = 8. 6023 (x 100) or 98 units or 8. 6023 units 76, 450, 379 = 76. 450379 x 106 or 76. 450379 Mega-units • Move the decimal point to the left in multiples of 3 places until only 1 to 3 digits remains to the left of it. • Multiply times 10+X where X is a multiple of 3 and the number of places the decimal point was moved to the left.

Engineering Notation – Numbers <1 Abbrev. Units Prefix Multiplier Power of 10 m milli- = x 10 -3 µ micro- = x 10 -6 n nano- = x 10 -9 p pico- = x 10 -12 Engineers only use powers of ten that are multiples of 3.

Examples Engineering Notation – Numbers <1 Number Engineering Notation 0. 6374 = 637. 4 x 10 -3 0. 00002473 = 24. 73 x 10 -6. 025398 = 25. 398 x 10 -3 0. 0000000271 = 27. 1 x 10 -9 or 637. 4 milli-units or 24. 73 micro-units or 25. 398 milli-units or 27. 1 nano-units • Move the decimal point to the right in multiples of 3 places until 1 to 3 digits remains to the left of it. • Multiply times 10 -X where X is a multiple of 3 and the number of places the decimal point was moved to the right.