Math with Sig Digs Review Notes and Practice
Name ____________________________________ Period ____
Review of Measured and Exact Numbers
Numbers obtained by using some type of measuring tool are called measured numbers. Numbers obtained from counting, or a definition, are exact numbers as they do
not require the use of a measuring tool. If you counted the number of people in the room, then that would be an exact number. If you make a conversion in the metric
system, then the numbers in the conversion (like 100 cm = 1 m) are also considered exact, as they come from a definition.
Rules for Significant Digits
1. All nonzero digits are significant.
2. Zeros between significant digits (sandwiched) are significant.
3. Zeros that are to the right of a decimal point AND to the right of a nonzero digit(s) are significant.
4. Any other zeros are only used as placeholders and are not significant.
Examples:
A. 455.2
4 Sig Digs
Rule 1
B. 0.80
2 Sig Digs
Rule 3
C. 50.20
4 Sig Digs
Rules 2 and Rule 3
D. 0.0005
1 Sig Dig
Rule 4
E. 25,000
2 Sig Digs
Rule 4
Review of Rounding Off
The results obtained from mathematical operations, such as addition, subtraction, multiplication, and division, are called calculated answers. The problem is that your
calculated answer cannot be more exact that your original measurements. Thus you must round off to an appropriate amount of significant digits (we’ll learn how to
determine this later.) Remember: if the first number to be dropped is a 5 or above, then round the number you are keeping up. If the first number to be dropped is a 4
or lower, then the number you are keeping stays as it is.
Examples:
Calculated Answer
Rounded to 3 Sig Digs
Rounded to 2 Sig Digs
A. 75.6243
75.6
76
B. 0.528392
0.528
0.53
C. 385,800
386,000
390,000
ALWAYS refer back to the original number.
Review of Multiplication and Division
A calculated answer from multiplication or division must be rounded off to match the significant digits of the measured number with the LEAST number of significant
digits. Remember: we do multiplication before division if both are involved in the same problem.
Example: Multiply 3.56 by 4.9.
From the calculator we see: 3.56 x 4.9 = 17.444
The measured number with the least sig digs is “4.9” – it has 2 sig digs
Thus the answer also gets rounded to 2 sig digs – 17.444 becomes 17
Example: Multiply 0.025 by 4.62 and divide by 3.44
From the calculator we see: 0.025 x 4.62 = 0.1155
Then from the calculator we see: 0.1155 ÷ 3.44 = 0.0335755
The measured number with the least sig digs is “0.025: - it has 2 sig digs
Thus the answer also gets rounded to 2 sig digs - .0335755 becomes .034
Review of Addition and Subtraction
Addition and subtract is very different from multiplication and division. A calculated answer must be rounded off to give a final answer with the same number of digits
as the measured number with the FEWEST digits AFTER the decimal point. DO NOT ADD IN ZEROS IF ZEROS ARE NOT GIVEN TO YOU.
Example: Add 42.11 to 30.1 to 4.056.
First line up the numbers:
42.11
+
30.1
+
_4.056_
Then do the addition:
76.266
Then find the fewest digits after the decimal
Then round the answer to match (in this case the tenth’s place) – 76.266 becomes 76.3
Example : Subtract 3.39 from 14.621
First line up the numbers:
14.621
3.39__
Then do the subtraction:
11.231
Then find the fewest digits after the decimal
Then round the answer to match (the hundredth’s place) – 11.231 becomes 11.23
State the number of significant digits in each of the following numbers.
A) 4.5 m
_______
D) 0.0250 L
_______
G) 1.0065 km
_______
B) 0.0004 L
_______
E) 204.52
_______
H) 82.05 g
_______
C) 805 lbs
_______
F) 625,000 mm
_______
I)
_______
0.04005000
Round each of the following numbers to 3 significant digits.
J)
98.473 _______________
K) 0.00076321
_______________
L) 57.048 _______________
O) 74.983 _______________
M) 9548
_______________
P) 1764.9 _______________
N) 12.17
_______________
Q) 8.859
_______________
Round each of the following numbers to 2 significant digits.
R) 98.473 _______________
V) 12.17
S) 0.00076321
W) 74.983 _______________
_______________
_______________
T) 57.048 _______________
X) 1764.9 _______________
U) 9548
Y) 8.859
_______________
_______________
Perform the following calculations. Give your final answer with the correct amount of Sig Digs.
Z)
4.5 x 0.28
_____________________
AA) 0.1184 x 8.0 x 0.034
_____________________
BB)
11.4 ÷ 2.3
_____________________
CC)
(42.4 x 5.6) ÷ 1.5
_____________________
DD) (35.56 x 1.45) ÷ (4.8 x 0.56)
_____________________
EE)
6.25 g + 0.683 g
_____________________
FF)
13.45 mL + 6.5 mL + 0.4552 mL _____________________
GG) 145.5 m + 86.58 m + 1045 m
_____________________
HH) 245.625 kg – 80.2 kg
_____________________
II)
4.62 cm – 0.885 cm
_____________________
State the number of significant digits in each of the following:
JJ)
48 cm
_____
NN) 71.60 g
_____
KK) 306.2 g
_____
OO) 0.00432 mm
_____
LL)
_____
PP)
_____
_____
QQ) 82.000 g
0.329 m
MM) 83.952 °C
10.0 kg
_____
Complete each of the following calculations, expressing the answer with the correct number of significant digits and label. To not
have the correct label will lose you points!
RR)
3.482 cm + 8.51 cm +16.324 cm
_______________
SS)
48.0032 g + 9.17 g + 65.4321 g
_______________
TT)
80.4 cm - 16.532 cm
_______________
UU)
106.5 mL - 30. mL
_______________
VV)
48.2 cm × 1.6 cm × 2.12 cm
_______________
WW)
8.3 m × 4.0 m × 0.9823 m
_______________
XX)
64.34 cm3 ÷ 8.149 cm
_______________
YY)
4.93 mm2 ÷ 18.71 mm
_______________
ZZ)
0.057 mL × 760 mm Hg ÷ 740 mm Hg × 273 K ÷ 250 K _______________
AAA)
51.3 g × 44.962 amu ÷ 115.874 amu
_______________
BBB)
5 cm + 0.03 cm + 2.0 cm
______________
CCC)
23.27 cm - 12.058 cm
______________
DDD)
350.0 g - 200 g
______________