Part 04 Rounding and Sig figs in Calculations page 25-26

What is the purpose of rounding? To limit the precision of a number. To make a number less specific. When you limit the precision of a number you need to start removing digits from right to left. When you get to the last digit to removed, that digit will indicate whether to round up or down. For example, round 5.66 to one decimal place. 5.7 For example, round 5.64 to one decimal place. 5.6Rounded down Rounded up These rounded numbers make sense because the answer is as close to the actual number as possible.

What happens when the last removed digit is a 5, which is not closer to rounding up or down? First, if there are any nonzero numbers to the right of this 5, then round up. This makes sense because this number is closer to the rounded up number If the last removed digit is a 5 and no nonzero numbers after it then…??? Then… round to the even number. This makes it 50/50 up/down. For example, round 5.65 to one decimal place. 5.6Rounded down For example, round to one decimal place. 5.7Rounded up

Round the following to three sig figs x Need the decimal! x

Sig figs in Calculations When multiplying/dividing, the answer must contain the same number of sig figs as the measurement with the LOWEST number of significant figures cm x 3.500cm = 19.2 cm 2 (55 m) 3 = m 3 2 x mm

Sig figs in Calculations When adding/subtracting, the answer must contain the same precision as the measurement with the LOWEST precision. Usually lowest precision = lowest number of decimal places cm – cm =2.00 cm m m =35.55 m 2400 ft ft. =3000 ft.

Sig figs in Calculations Exact numbers have an infinite number of sig figs so they are never the LOWEST sig figs or precision. You can ignore them when finding the lowest. Exact numbers are counting numbers like how many students are in the class right now. Also, defined numbers like there are 12 inches in 1 ft or 60 seconds in 1 minute.

Assignment Worksheets 02 and 03: p 7-8