# 1. Yes 2. No  Accuracy - How close a measurement is to the true value  Precision - How close a set of measurements are to one another.

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1. Yes 2. No

 Accuracy - How close a measurement is to the true value  Precision - How close a set of measurements are to one another.

1. Accurate 2. Precise 3. Both 4. Neither

1. Accurate 2. Precise 3. Both 4. Neither

1. Accurate 2. Precise 3. Both 4. Neither

Write each power of ten in standard notation. 10 3 a)30 b)100 c)1000

Write each power of ten in standard notation. 10 6 a)60 b)1000000 c)10000

Write each power of ten in standard notation. 10 -2 a).01 b)-20 c)100

Write each power of ten in standard notation. 10 -4 a)-.0004 b).0004 c)10000

Setting the Stage There are 325,000 grains of sand in a tub. Write that number in scientific notation.

What is the exponent to the 10 for 325,000 grains of sand? 1.3 2.4 3.5 4.6 5.-6 6.-5 7.-4

Definition Scientific notation- is a compact way of writing numbers with absolute values that are very large or very small. Glencoe McGraw-Hill. Math connects cours 3. pages 130-131

 all numbers are expressed as whole numbers between 1 and 9 multiplied by a whole number power of 10.  If the absolute value of the original number was between 0 and 1, the exponent is negative. Otherwise, the exponent is positive. Ex. 125 = 1.25 x 10 2 0.00004567 = 4.567 x 10 -5

1. -6 2. 6 3. -5 4. 5 5. 4 6. -4

1. -6 2. 6 3. -5 4. 5 5. 4 6. -4

What is 2.85 x 10 4 written in standard form A..000285 B.285 C.28500 D.2850

What is 3.085 x 10 7 written in standard form A..0000003085 B.30,850,000 C.3085 D.308,500,000

What is 1.55 x 10 -3 written in standard form A..00155 B.155 C.1550 D..000155

What is 2.7005 x 10 -2 written in standard form A.270.05 B.27005 C..27005 D..027005

Write the following numbers in scientific notation: A) 5,000E) 0.0145 B) 34,000F) 0.000238 C) 1,230,000G) 0.0000651 D) 5,050,000,000H) 0.000000673

Closure / Summary Explain why 32.8 x 10 4 is not correctly written in scientific notation. What does a negative exponent tell you about writing the number in standard form.

 Significant Figures are used to show the accuracy and precision of the instruments used to take the measurement.

0 1 0 0 1 1.5

0 1 1. 0.55 2. 0.7 3. 0.6 4. 0.8

0 1 1. 0.55 2. 0.70 3. 0.67 4. 0.65

 To show how precise the instrument is: Read the measurement to one decimal place what the instrument is marked

1. 4.85 2. 7.2 3. 4.3 4. 4.35

1. 17.0 2. 16.8 3. 15.18 4. 15.2

 Non-zero digits are always significant 1,2,3,4,5,6,7,8,9 are always significant  Rules for Zeros: a) Leading Zeros never count as significant 0.00004560.0032 b) Captive zeros (zeros between non-zero digits) are always significant 10,0340.005008 c) Trailing Zeros are significant ONLY IF there is a decimal in the number. 234,000234,000.00.045600

 If we want to write the number 700 with 3 significant digits we can do so using the following two methods: 700. OR 7.00×10 2

How many significant digits do the following numbers have? A) 20F) 7.00K) 65,060 B) 22.0G) 87,001L) 0.9090 C) 20.1H) 0.00018M) 18.01 D) 56,000I) 0.0109N) 4.30×10 4 E) 75,000.J) 570O) 0.0001

1. 1 2. 2 3. 3 4. 0

1. 0 2. 1 3. 2 4. 3

1. 3 2. 1 3. 6 4. 7 1234567891011121314151617181920 2122

1. 0 2. 1 3. 2 4. 3 1234567891011121314151617181920 2122

1. 2 2. 5 3. 1 4. 3 1234567891011121314151617181920 2122

1. 1 2. 2 3. 3 4. 4 1234567891011121314151617181920 2122

1. 1 2. 2 3. 3 4. 4 1234567891011121314151617181920 2122

1. 5 2. 8 3. 2 4. 4 1234567891011121314151617181920 2122

1. 5 2. 8 3. 2 4. 4 1234567891011121314151617181920 2122

1. 3 2. 8 3. 4 4. 5 1234567891011121314151617181920 2122

You and a partner will practice your significant digits. Your job is to come up with a number containing both zeroes and non-zero digits. You will trade boards back and forth – on my mark. The partner that gets the correct number of significant digits will get the point. The partner with the most points will win the round. We will do best of 9.

 Count (from left to right) how many significant figures you need.  Look at the next number to see if you need to round your last sig. fig. up or down. Round the following to 3 sig. figs 1. 1,344 2. 0.00056784 3. 24,500 4. 12,345 5. 2.45678 x 10 -3

We have two ways of categorizing sig. fig. calculations: A) Addition and Subtraction B) Multiplication, Division, other math

When we add and subtract we are only worried about the number of decimal places involved in the numbers present. We do not care about the number of actual significant digits. We will always pick the number that has the least decimal places.

A) 14.0 + 2.45 B) 12 + 7.2 C) 0.00123 + 1.005 D) 100 – 5.8 E) 2.5 – 1.25 F) 43.786 – 32.11

If we are multiplying, dividing, using exponents, trigonometry, calculus, etc we must use the least number of significant digits of the numbers in the set. For example...

A) 12 × 5.00F) 119 / 32 B) 8.45 × 4.3G) 756.2 / 29.8 C) 0.0125 × 7.532H) 0.976 / 0.0044 D) 5.6 × 11.7I ) 981 / 756.23 E) 34.1 × 0.55J) 43.2 / 12.45

 Density – the amount of matter present in a given volume of a substance, the ratio of the mass of an object to its volume.  D = mass  Volume

 Celsius Scale – based on the freezing point (0 o C) and boiling point (100 o C) of water.  Kelvin Scale – based on absolute zero (the temperature at which all motion ceases). 1 degree Kelvin is equal to 1 degree Celsius.  Fahrenheit Scale – used in US and Great Britain. Degrees are smaller than a Celsius or Kelvin degree.

 Kelvin/Celsius K = o C + 273  Fahrenheit/Celsius o F = 1.80( o C) + 32

 Exact Numbers are counting numbers or defined numbers (such as 2.45 cm = 1 in) - never limit the number of significant figures in a calculation.

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