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
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
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...
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.