Learning Goals convert numbers to scientific notation convert measurements using the metric system identify the number of significant digits in a measurement Scientific Notation ID: 265102
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Slide1
Scientific Notation, Conversions and Significant Digits
Learning Goals …
… convert numbers to scientific notation
… convert measurements using the metric system
… identify the number of significant digits in a
measurement Slide2
Scientific Notation
Ex) Convert the following to scientific notation:
(a) 0.000053 = ______________________ (b) 40 000 000 = ____________________ (c) (2.63 x 10-9)(5.06 x 103) = ______________Note: use the exponent button on your calculatorEXP, E, EE
5.3 x 10-5
4.0 x 107
1.33 x 10-5
Try working on
Practice Questions
…Slide3
Practice Questions:
Express the following numbers in scientific notation:
1003000000000 = _________________________0.0000000003998 = _________________________ 58.23 = _________________________ 0.2038 = _________________________ 12452 = _________________________Express the following numbers to decimal notation:1.77 x 107 = ________________________ 2.552 x 10-9 = _________________________
1.18 x 103
= _________________________
4.44 x 10
-1
= _________________________ 1.399 x 100 = _________________________Express the results of the following operations in scientific notation:1.39 x 10-2 + 3.11 x 10-4 = _________________________ 1.17 x 104 - 3.57 x 102 = _________________________ (1.81 x 10-3) (1.06 x 1020) = _________________________ (5.77 x 10-4) (1.71 x 10-11) = _________________________
1.003 x 1012
3.998 x 10-10
5.823 x 101
2.038 x 10-1
1.2452 x 104
17700000
0.000000002552
1180
0.444
1.399
1.42 x 10-2
1.13 x 104
1.92 x 1017
3.37 x 10
7Slide4
Volume
Cubic units (m
3, cm3, mm3) Vs. Capacity units (mL, L, kL) Cubic units can be converted to capacity units (and vice versa) using the following conversions: 1 cm3 = 1mL 1000 cm3 = 1000
mL = 1 L
1 m
3 = 1000 L
1 m
3 = (100cm)(100cm)(100cm)1 m3 = 1000000 cm3 = 1000000mL1 m3 = 1000 LSlide5
k
(kilo)
h(hecta)da(deca)unitd(deci)c
(centi
)
m
(
milli)The Metric System:Convert the following:3.15 m = __________ cm g) 15.5 mg = ____________ g955 g = ___________ kg h) 1620 km = ___________ dm 1630 mL = _________ L
i) 144 kg = _____________ mg
20.0 hg = __________ mg j) 0.0117 mm = __________ cm
178 mm = _________ cm k) 3450 cm
3
= ____________ L
2000 L = ______
m
3
l) 126 m
3 = ____________ cm
3
315
0.955
1.630
2 000 000
17.8
2
0.0155
16 200 000
144 000 000
0.00117
3.450
126 000 000
x 10 x 10 move decimal to
the right
÷10 ÷10
move decimal to
the leftSlide6
Significant Digits
Non-zero digits are always significant.
(eg) 22 ______ significant digits 22.3 ______ significant digitsWith zeros, the situation is more complicated: Zeros placed before other digits are not significant (place holders)(eg) 0.046 ______ significant digits
(
eg
) 0.005487 g ______ significant digits
Zeros placed between other digits are
always significant.(eg) 20.64 L ______ significant digits(eg) 4009 kg ______ significant digits232444Slide7
Zeros that exist after the decimal place to demonstrate accuracy
are
significant.(eg) 46.20 ______ significant digits(eg) 3.000 ______ significant digitsZeros that exist at the end of a number are significant only if they are behind a decimal point. If the zeros at the end of a number do not follow a decimal point, they are not significant (place holders)(
eg
) 382 000 ______ significant digits
(
eg
) 382 000.0 ______ significant digits4437Slide8
Measurement
Certainty
MeasurementCertainty522.3 cm sig digs0.0250 cm
sig digs
12 m/s
sig digs3.10 x 105 m/s sig digs0.005 km sig digs
0.06070 m
sig digs
If you have an
exact
value or
defined
value, the significant digits are
infinite
Ex. 5 cats 10 chairs 60 min/h 1000m/km
4
2
1
3
3
4Slide9
ROUNDING
If the digit after the digit to be retained as significant is a
greater than 5, round upIf the digit after the digit to be retained as significant is a 4 or less, round downIf the digit after the digit to be retained as significant is exactly 5:if the digit to be retained is odd, round upif the digit to be retained is even, round downRound the following to a whole number:91.8
_______
d)
78.58 _______
52.3
_______ e) 42.5 _______37.53 _______ f) 37.5 _______ 925238794238Slide10
CALCULATIONS INVOLVING SIGNIFICANT DIGITS
ADDITION AND SUBTRATION
Precision Rule – Precision is defined as the place value of the last digit obtained from a measurement or calculationWhen adding or subtracting, the final answer has the same number of decimal places as the number with the least number of decimal places. The least number of decimal places is ____ (eg) 6.6 m + 18.74 m + 0.766 m = __________________ 26.11Slide11
Multiplication and Division
When
multiplying or dividing, the final answer must have the same number of significant figures as the original number with the fewest significant figures (we can’t be any more certain than we were to begin with)(eg) Calculate the volume of a box with sides measuring 5.05 cm, 3.87 cm and 4.7 cm V = (5.05 cm x 3.87 cm x 4.7 cm) = 91.85445 cm3 = 92 cm3Slide12
HOMEWORK
WS “Significant Digits”
Complete any Practice Questions CAN I …… convert numbers to scientific notation… convert measurements using the metric system… identify the number of significant digits in a measurement