Name: ________________________________________________
COMMUNICATION SKILLS
Date: _______________________________
Significant Digits



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
 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 10 3 = 1.934 x 10 4 , etc.)
Converting Metric Units

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
R/I 1 2 3 4
Using the Factor Label method
 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
1. How many significant digits are these in each of the following measurements? a) 2.258 cm c) 0.00024 mm e) 2.036 x 10 -4 s g) 368000000 m i) 38.63000 kg
4
2
4
3
7 b) 2040mg d) 5.69 x 10 3 um f) 9.80 x 10 -4 m h) 0.020050 km j) 680g
3
3
3
4
2
2.
Round each value to 3 significant digits. a) c) e)
1.477 cm
0.0002589 mg
32650000a (years)
1.48 cm b) 283.508 cm
0.000259 mg d) 8.0175 x 10 3 um
3260000a f) 9.999 x 10 -4 m
5.70 m h) 87.6510 km
283.508 cm
8.02 x 10 3 um
1.00 x 10 -3 m
87.7 km g) 5.69505 m i) 25.65900 km 25.7 km j) 26549Mb 26500Mb
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:
1) The answer (product/quotient) has the same number of significant digits as the factor with the least number of significant digits

2) Determine the answer (product/quotient) first, then determine the round off to the correct number of significant digits. a) 8.73 cm X 4.5 cm= 39 cm 2 b) 2200 m X 830 m= 1800000 m 2 = 1.8 x 10 6 m 2 c) 4.256 mol X 232.46g/mol= 989.3g d) 0.00342 mol X 100.09 g/mol= .342g e) 4.7 mol X 6.02 x 10 23 molecules/mol= 2.8 x 10 24 molecules f) 0.0096 mm 2 / 0.890 mm= .011mm g) 75g / 196 cm 3 = 0.38g/cm 3 h) 0.0450 g / 0.00025 mol = 180 g/mol i) 32.525 m / 6.753s= 4.816 m/s
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 adding or subtracting with significant digits are:
1) Determine which addend in the question is the least accurate. Round off all addends to the same decimal place value. Then add/subtract. (Note that we are NOT counting significant digits we are more concerned with place value)
2) Round off the addends then add
LOOK AT THE RUBRIC – YOU GET CREDIT FOR SHOWING YOUR WORK!
a) 2556.1 cm + 325. 318 cm + 13.12 cm d) 10,000.1 m→ 10,000.1 m b) 290.7 cm – 177.45 cm c) 72.605 m + 253.66 m d) 10,000.1 m – 940.23 m e) 8.9 x 10 3 m + 2.68 x 10 4 m f) g)
8.0890 cm – 10.066 cm
5.62 cm + 10.29 cm
– 940.23 m→– 940.2 m e) 8.9x 10 3
9059.9 m
m→ .89 x 10 4 m
+ 2.68 x 10 4 m→+ 2.68 x 10 4 m
3.57 x 10 4 m
(you must have the same exponent a) 2556.1 cm → 2556.1 cm
325.318 cm → 325.3 cm to be able to add exponents)
+ 13.12 cm → 13.1 cm
2894.5 cm b) 290.7 cm→ 290.7 cm
– 177.45 cm→ 177.4 cm c) 72.605 m→
113.3 cm
72.60 m
+ 253.66 m→ 253.66 m
326.26 m f) 8.0890 cm→ 8.089 cm
– 10.066 cm→– 10.066 cm
- 1.977 cm g) 5.62 cm→5.62 cm
+ 10.29 cm→+ 10.29 cm
15.91 cm
1. Convert each number from standard form to scientific notation with the correct number of significant digits.
Remember to record digits.
Standard Form a) 132000 m
Scientific Notation
1.32 x 10 5 m
Standard Form b) 600
Scientific Notation
6 x 10 2 c) 0.0009872 9.872 x 10 -4 d) 0.0000000360 3.60 x 10 -8

e) 56000000 5.6 x 10 7 f) 78856000 7.8856 x 10 7 g) 0.0035608 3.5608 x 10 -3 h) 0.000065690 6.5690 x 10 -5 i) 96, 000 c)
63000000
9.6x 10 4
6.3 x 10 7 j) d)
8565000000
0.00888659
8.565 x 10 9
2. Convert each number from scientific notation to standard form with the correct number of significant digits.
Remember to record digits. a)
Standard Form
0.0000235
Scientific Notation
2.35 x 10 -5 b)
Standard Form
5600000
Scientific Notation
5.6 x 10 6
8.88659 x 10 -3 e) 0.00786 g)
95680 i)
0.00000001365
7.86 x 10 -3
9.568 x 10 4 f) 569800000 h) 0.0968
5.698 x 10 8
9.68 x 10 -2
1.365 x 10 -8
_0.0025_ Gb j) 0.0000000235 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) multiply the coefficients first then multiply the exponents (format: a x 10 b – where a is the coefficient and b is the exponent)
2) if multiplying, add exponents; if dividing , subtract exponents.
3) The coefficient must be between 1 and less than 10. If the coefficient is less than 1, slide the decimal to the right and lower the exponent by 1. If the coefficient is greater than 1, slide the decimal to the left and increase the exponent by 1. (ex. 23.6 x 10 2 = 2.36 x 10 3 ) a) 2.3 x 10 -5 cm X 4.5 x 10 6 cm= 10.35 x 10 1 = 1.035 x 10 2 = 1.0 x 10 2 cm 2 (showing all the steps) b) 4.25 x 10 -6 mol X 2.3246 x 10 2 g/mol= 9.88 x 10 -4 g c) 4.71 x 10 12 m÷ 3.125 x 10 7 sec = 1.51 x 10 5 m/sec d) 3.42 x 10 -3 molX 1.0009 x 10 2 g/mol= 3.42 x 10 -1 g e) 54285g ÷ 2.55 x 10 3 cm 3 = 2.13 x 10 1 g/cm 3 f) 4.72 x 10 21 molecules ÷ 6.02 x 10 23 molecules/mol= 7.82 x 10 -3 mol g) 3.65 x 10 6 cm X 8.7 x 10 4 cm ÷ 3.76 x 10 -4 cm= 8.44 x 10 14 cm
a) 2.764 g _0.002764_ kg b) 43 mmol _0.043_mol c) 2500 Kb d) 0.0000000360km _36_µm e) 2.50 x 10 6 m g) 3.75 x 10 -5 m
_ 2.50 x 10 3 _ km
_ 3.75 x 10 -5 _ cm f) 78, 856, 000 ML h) 0.65690 kg
_ 78856000000000 _ L
_ 65690 _ mg i) 2.26 x 10 -7 mg _ 2.26 x 10 -13 _ kg j) 834500 cm _8345_ m
Use dimensional analysis to solve the following questions:
1.
The density of mercury metal is 13.6 g/mL. What is the mass of 3.55 mL of the metal?
13.6g 3.55 mL 48.3g mL
2.
A particle moves through a gas at a speed of 15 km/s. How far will it move in 5.5 s?

15 km 5.5 s s
3.
Convert 76.3 km/h into m/s?
76.3 km 1000 m
82 km
1 h 1 min 21.2 m h km 60 min 60 sec sec
4.
How many seconds are there in 1 year? (convert from s to min to h to d (days) to a (years) - there are 365.23 days per year). Convert your answer to scientific notation.
365.23 d 24 h 60 min 60 sec 31556000 sec a d 1 h
5.
The speed of light is 299792458 m/s.
1 min a a) How far can light travel in 25.3 minutes?
25.3 min 60 s 299792458 m 455000000000 m = 4.55 x 10 11 m min s b) The average distance from the Sun to the Earth is 1.496 x 10 8 km. How long does it take for light from the sun to reach the Earth?
1.496 x 10 8 km 1000 m s 499.1 s 1 min 8.317 min km 299792458 m 60 s
6.
Gold costs 1418.07 per ounce (in Canadian dollars (March 31, 2014)). 1 ounce is equal to 28.35 grams. The size of a standard gold bar is 17.78 cm x 9.208 cm x 4.445 cm. The density of gold is
19.32 g/cm 3 . What is the value of a gold bar in Canadian dollars?
17.18 cm 9.208 cm 4.445 cm 19.32 g 1 oz $1418.07 $679500 cm 3 28.35 g oz
7.
Canada’s Hemlo Gold mine extracted 3000 tonnes of rock every day. The gold ore contained 10.4 g of gold per tonne. How many dollars’ worth of gold did they produce every day?
3000 tonnes 10.4 g 1 oz $1418.07 $1560000 d tonne 28.35 g oz d