Transcript 3.1 Using and Expressing Measurements - Falcon Science
1 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.
3.1 Using and Expressing Measurements >
2
Scientific Notation
• A *
measurement
is a has both a
number
quantity that and a
unit
.
In
scientific notation
, a given number is written as the product of two numbers = a coefficient x 10 n *n = exponent Example: 602,000,000,000,000,000,000,000 6.02 x 10 23
3.1 Using and Expressing Measurements >
Scientific Notation
How to Write in Scientific Notation
If the coefficient
>
10 Decimal moves to the left # spaces = n + 6,300,000. = 6.3 x 10 6 If the coefficient < 1 Decimal moves to the right # spaces = n 0.000 008 = 8 x 10 -6 94,700. = 9.47 x 10 4 0.00736 = 7.36 x 10 -3 3 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.
3.1 Using and Expressing Measurements >
Practice Problems #1: Write the following in scientific notation.
① 3,400 = ② ③ 101,000 = 45.01 = ④ ⑤ 0.000023 = 0.010 = ⑥ 1,000,000 = 4 ***DO PRACTICE PROBLEMS ON THE BOARD*** Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.
5
3.1 Using and Expressing Measurements >
***REMEMBER*** Move the decimal point until you have
1 WHOLE NUMBER
to the
LEFT OF DECIMAL POINT
!
Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.
6
3.1 Using and Expressing Measurements >
Scientific Notation
Multiplication and Division
To multiply: multiply the coefficients and add the n.
(3 x 10 4 ) x (2 x 10 2 ) = (3 x 2) x 10 4+2 = 6 x 10 6 (2.1 x 10 3 ) x (4.0 x 10 –7 ) = (2.1 x 4.0) x 10 3+( –7) = 8.4 x 10 –4 To divide: divide the coefficients and subtract the n(numerator – denominator).
3.0 x 10 5 6.0 x 10 2
=
( 3.0
6.0
) x 10 5 –2
=
0.5 x 10 3 = 5.0 x 10 2
3.1 Using and Expressing Measurements >
Practice Problems #2: Solve the following problems and write your answers in scientific notation.
① ② ③ ④ ⑤ (8.0 x 10 –2 ) x (7.0 x 10 –5 ) = (6.6 x 10 6 ) (5.0 x 10 6 ) (2.2 x 10 (2.0 x 10 2 4 ) = ) = (3.0 x 10 –3 ) x (2.5 x 10 –4 ) = (8.8 x 10 –2 ) x (2.5 x 10 3 ) = 7 ***DO PRACTICE PROBLEMS ON THE BOARD*** Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.
3.1 Using and Expressing Measurements >
Significant Figures
*Significant Figures
• The
significant figures
in a measurement include all of the digits that are known, plus a last digit that is estimated.
8
3.1 Using and Expressing Measurements >
Significant Figures
Rules of Significant Figures
1. Every nonzero digit is significant.
24.7 m 0.743 m 714 m 2. Zeros appearing between nonzero digits are significant.
7003 m 40.79 m 1.503 m 9
3.1 Using and Expressing Measurements >
Significant Figures
Determining Significant Figures in Measurements
3. All zeros on the left are not significant. To eliminate, write the number in scientific notation.
0.0071 m = 7.1 x 10 -3 m 0.42 m = 4.2 x 10 -1 m 0.000 099 m = 9.9 x 10 -5 m 4. To be significant, Zeros must be after a number and after the decimal point.
43.00 m 1.010 m 9.000 m 10 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.
3.1 Using and Expressing Measurements >
Significant Figures
Determining Significant Figures in Measurements
5. Zeros in front of the decimal point are not significant.
300 m 7000 m 27,210 m If zeros were exact measurements, then they’re significant. Write the value in scientific notation.
300 m = 3.00 x 10 2 m 11 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.
3.1 Using and Expressing Measurements >
Practice Problems #3: Determine the number of sig figs.
① ② ③ ④ ⑤ ⑥ 6.571 g 2500 m 0.157 kg 0.0700000 g 28.0 ml 30.07 g 12 ***DO PRACTICE PROBLEMS ON THE BOARD*** Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.
3.1 Using and Expressing Measurements >
Significant Figures
Significant Figures in Calculations Rounding
• 1. decide how many significant figures • 2. round to that many digits • Note: • If the next number is <5, digit stays the same.
• If the next number is ≥5, round up.
For Example: a. 314.721 m (four) b. 0.001 775 m (two) c. 8792 m (two) 314.7 m 0.0018 8800 3.147 x 10 2 m 1.8 x 10 -3 m 8.8 x 10 3 m 13
3.1 Using and Expressing Measurements >
Significant Figures
Significant Figures in Calculations Multiplication and Division
• Round the answer to the
same number of significant figures as the measurement with the least number of significant figures
.
7.55 m x 0.34 m = 2.567 m 2 = 2.6 m 2 14 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.
3.1 Using and Expressing Measurements >
Practice Problems #4: Solve the following problems. Write the answers in the correct number of sig figs and in scientific notation.
① ② ③ 2.10 m x 0.70 m 0.365 m 2 2.4526 m 2 0.0200 m 8.4 m ④ 8.3 m x 2.22 m 15 ***DO PRACTICE PROBLEMS ON THE BOARD*** Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.