## Friday, October 29, 2010

### Significant Figures and Rounding: Questions & Answers

1. Write down the significant figure specified in the bracket:

a) 47.351 (2nd)
The second s.f. is 7. Note the question asks for the 2nd digit, not two digits. A common mistake
was to round the number to 2 s.f.

b) 0. 01230 (3rd)

The third s.f. is 3. Leading zeros are not mathematically significant, and are simply “place-holders.”

2.Give the following correct to the accuracy given in the brackets:
a) 5972 to 1 s.f. is 6000

b) 809.317 to the nearest 10 is 810

c) 0.04065 to 3 s.f. is 0.0407

d) 0.08374 to 2 d.p. is 0.09, or simply .09

3. To the nearest 100, attendance at the School Carnival was 2300.
a) What is the maximum number who could have attended?
“To the nearest 100” means “plus or minus 50”.
2300 + 50 equals 2350. However this could not have been the actual attendance. If 2350 was the true figure the attendance would have been given as “2400 to the nearest 100.” But it wasn't. So the true maximum must be 2349. (Under the assumption that the commom rounding convention for 5s has been used.)
b) What is the minimum number who could have attended?
The minimum number of people who attended could be 2300 – 50 = 2250.

4. Estimate the following calculations. (Show all workings.)
a) 596 / 9.12 To one s.f. each this becomes 600/10 = 60

b) 16.5 * 14.4 To one s.f. each this becomes 20 * 10 = 200. If you are good with squares you might say its about 15 * 15 = 225.

5. Douglas wants to save RM 1850 by putting the same amount of money into a savings account for 26 weeks.
a) Estimate how much he should save each week. (Show all workings.)

There are several approaches:
1 s.f. each gives RM 2000/30 = 200/3 = 66 --> 70 to 1 s.f.
Or using 2 s.f., note that 26 is close to 25 and that 100 is 4 * 25:
1850/26 ~ 1900/25 = (19 * 4 * 25)/25 = 19*4 = 76

b) Do you think you estimate is too large, too small, or about right? Explain why.

RM 70 is about right, because 70 * 26 = 1820 which is very close to the original figure of RM1850.
Although the \$76 estimate seems clever, it actually may not be. Because it is much harder to mentally calculate 76 * 26, you will probably skip this step where you check if your estimate is 'too large, too small, or about right'. Potentially costly, if you accept a caculator answer that is the result of incorrectly keyed in data and/or operations. Two acronyms to remember:
• K.I.S. = Keep It Simple
• G.I.G.O. = Garbage In, Garbage Out