SCH 3UI Math Worksheet
Name: ________________________________________________
Date: _______________________________
COMMUNICATION SKILLS
Significant Digits
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R/I
1
2
3
The student identifies the number of significant digits
When adding or subtracting, the student identifies the least accurate value.
When adding or subtracting , the student rounds each value to the same number of decimals
BEFORE adding or subtracting.
When multiplying or dividing, the student identifies the value with the least number of
significant digits.
When multiplying or dividing, the student rounds the ANSWER to the same number of
significant digits as the least accurate value (MULTIPLY/DIVIDE THEN ROUND)
Scientific Notation
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The student consistently andmeticulouslyusesproper scientific notation (exponents magnitude
and symbol, coefficient decimal location)
The student is able to apply proper strategies when multiplying and dividing values expressed
in scientific notation (ex. multiply co-efficients first then multiply the bases (by adding the
exponents), converting answers – 19.34 x 103 = 1.934 x 104, etc.)
Converting Metric Units
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The student understands the metric conversion chart to enable the determination of how many
places the decimal must be moved.
The student understands which way the decimal must be moved
Using the Factor Label method
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A.
The student sets up a factor label method properly with the key value in the first square
The student records units (and compound names) in each square
The student is able to make conversions properly (placing the values in the correct box so that
the units cancel
The student provides the correct number of significant digits in the answer
Significant Digits
1. How many significant digits are these in each of the following measurements?
a)
c)
e)
g)
i)
2.258 cm
0.00024 mm
2.036 x 10-4 s
368000000 m
38.63000 kg
2. Round each value to 3 significant digits.
a)
1.477 cm
c)
0.0002589 mg
e)
32650000a (years)
g)
5.69505 m
i)
25.65900 km
b)
d)
f)
h)
j)
2040mg
5.69 x 103 um
9.80 x 10-4 m
0.020050 km
680g
b)
d)
f)
h)
j)
283.508 cm
8.0175 x 103 um
9.999 x 10-4 m
87.6510 km
26549Mb
3. Multiply or Divide the following values. Make sure that your answer has the correct number of
significant digits and the correct units. You may need a rough work page.
Two things to remember when multiplying or dividing with significant digits are:
4
1)
2)
a)
b)
c)
d)
e)
f)
g)
h)
i)
8.73 cm X 4.5 cm
2200 m X 830 m
4.256 mol X 232.46g/mol
0.00342 mol X 100.09 g/mol
4.7 mol X 6.02 x 1023 molecules/mol
0.0096 mm2 / 0.890 mm
75g / 196 cm3
0.0450 g / 0.00025 mol
32.525 m / 6.753s
4. Add or Subtract the following values. Make sure that your answer has the correct number of
significant digits and the correct units. You WILL need a rough work page.
Two things to remember when multiplying or dividing with significant digits are:
1)
2)
a)
b)
c)
d)
e)
f)
g)
B.
1.
2.
2556.1 cm + 325. 318 cm + 13.12 cm
290.7 cm – 177.45 cm
72.605 m + 253.66 m
10,000.1 m – 940.23 m
8.9 x 103 m + 2.68 x 108 m
8.0890 cm – 10.066 cm
5.62 cm + 10.29 cm
Scientific Notation
Convert each number from standard form to scientific notation with the correct number of significant digits.
Remember to record digits.
Standard Form
Scientific Notation
Standard Form
Scientific Notation
a) 132000 m
b)
600
c) 0.0009872
d)
0.0000000360
e)
56, 000, 000
f)
78, 856, 000
g)
0.0035608
h)
0.000065690
i)
96, 000
j)
8, 565, 000, 000
Convert each number from scientific notation to standard form with the correct number of significant digits.
Remember to record digits.
Standard Form
Scientific Notation
Standard Form
Scientific Notation
-5
a)
2.35 x 10
b)
5.6 x 106
c)
6.3 x 107
d)
8.88659 x 10-3
e)
7.86 x 10-3
f)
5.698 x 108
g)
9.568 x 104
h)
9.68 x 10-2
i)
1.365 x 10-8
j)
2.35 x 10-7
3.
Multiply or Divide the following values. Make sure that your answer has the correct number of
significant digits and the correct units. You may need a rough work page.
Two things to remember when multiplying or dividing with scientific notation are:
1)
2)
a)
b)
c)
d)
e)
f)
g)
C.
2.3 x 10-5cm X 4.5 x 106cm
4.25 x 10-6mol X 2.3246 x 102g/mol
4.71 x 1012 m÷ 3.125 x 107 sec
3.42 x 10-3molX 1.0009 x 102 g/mol
54285g ÷ 2.55 x 103 cm3
4.72 x 1021 molecules ÷ 6.02 x 1023 molecules/mol
3.65 x 106cm X 8.7 x 104cm ÷ 3.76 x 10-4 cm
Converting metric (SI – System international) units
a)
2.764 g
___________ kg
b)
43 mmol
c)
2500 Kb
d)
0.0000000360km
e)
2.50 x 106 m
f)
78, 856, 000 ML
g)
3.75 x 10-5 m
___________ Gb
___________ km
___________ cm
h)
0.65690 kg
___________ L
___________ mg
i)
2.26 x 10-7 mg
___________ kg
j)
834500 cm
___________ m
___________ mol
___________ µm
Significant Digits Practice Problems Level 3
1. How many significant digits are there in each of the following measurement?
a. 307 g
f. 350,000 cm
b. 1.40082 cm
g. 180.00 s
c. 0.00058900 g
h. 3.50 X 103 cm
d. 0.00300900870 mm
i. 1.604 X 10-4 m
e. 4500 km
j. 0.0459 X 103 g
2. Express the answer to each of the following calculations with the correct number of significant digits.
a. 80 cm + 13.0 cm
f. 750 cm - 677.4 cm
b. 72.60 m + 0.0950 m
g. 10,000 m - 940 m
c. 13.89 cm + 6.8932 cm
h. 0.0890 cm - 0.0666 cm
d. 1.30 X 10-2 cm + 2.4 X 10-4 cm
i. 0.340 X 10-1 g - 1.20 X 10-2 g
e. 8.99 X 103 m + 1.400 X 104 m
j. 4.5 X 105 km - 3.00 X 103 km
3. Express the answer to each of the following calculations with the correct number of significant digits.
a. 3.0 cm X 4.000 cm
f. 0.0045 mm2 ÷ 0.90 mm
b. 2.005 cm X 5.0 cm
g. 120 km2 ÷ 8.56 km
c. 400 m X 87,488 m
h. 0.7600 mm3 ÷ 1.50 mm
d. 2.3 X 10-6 m X 1.45 X 10-2 m
i. 4.80 X 105 m2 ÷ 8.5 X 103 m
e. 8.70 X 10-2 mm X 40 X 10-1 mm
j. 0.630 X 10-1 m3 ÷ 0.0804 X 102 m