Do this (without a calculator!) 42.5 x 37.6

1. Do this (without a calculator!) 42.5 x 37.6

2. Slide Rules A blast from the past

5. Logarithms were invented by the Scottish mathematician and theologian John Napier and first published in 1614. He was looking for a way of quickly solving multiplication and division problems using the much faster methods of addition and subtraction. Napier's way of doing this was to invent a group of "artificial" numbers as a direct substitute for real ones.

6. He called this numbering system logarithms (which is Greek for "ratio-number", apparently). Logarithms are consistent, related values which substitute for real numbers. Incidentally, it wasn't until a few years later, in 1617, that a fellow mathematician named Henry Briggs adapted Napier's original "natural" logs to the more commonly used and convenient base 10 format.

7. Source: http://www.sliderule.ca/intro.htm • To see how these are useful for multiplication, consider what happens if you want to multiply 10 x 1,000, as a simple example. The secret here is that you could just add their logs together and then take the anti-log of the result. • Why? Because log xy =

9. How do logs help in multiplication? 2 x 3 = y Log (2 x 3) = log y Log 2 + log 3 = log y .301 + .477 = log y .778 = log y 10.778= y y = 6

10. To find log x: 1. Line up cursor with x on D scale 2. Read number on L scale 3. Add “1” to your answer for each number past the ones place Ex. Find log 25 Line up cursor with 2.5 on D scale Read number on L scale Because there’s a number in the 10’s spot, add 1.

11. Use the slide rule to find the following logs. 1. Log 3 2. Log 8 3. Log 1.2 4. Log 38 5. Log 52 6. Log 135

12. What number has a log of. . . 1. 0.6 2. 1.37 3. 2.2

13. To multiply (xy): • Line up "1" of C scale with x on D scale • Set hairline of cursor over y on C scale. • Answer is number on D scale Ex. Multiply 2x3: Line up "1" on C scale with 2 on D-scale Move cursor to 3 on C scale Read # on D scale

14. Do these: • 15 x 4 • 18 x 3.7 • 1.5 x 2.3 • 280 x 0.34 • .0215 x 3.54

15. To divide ( x ÷ y ): • Line up x on D scale with y on C scale. • Answer lines up with “1” on D scale. Ex. Divide 8 ÷ 4 • Line up 8 on D scale with 4 on C scale • Move cursor to 1 on C scale • Read # on D scale

16. Do these: • 15 ÷3 • 62.4 ÷ .707 • 23 ÷ 1.6 • 0.53 ÷ 7

17. Combining Operations • Think of problem as • Line up x on D scale with z on C scale 3. Move cursor to y on C scale 4. Read answer on D scale

18. Do these: 1. 2. 3. 4.