Significant Digits Coordinate Algebra

Determining the number of significant digits Numbers with a decimal point: count the digits from left to right starting with the first nonzero digit and ending with the last digit Numbers without a decimal point: count from left to right starting with the first digit and ending with the last nonzero digit

Basic Rules for Significant Digits All nonzero (1-9) digits are significant All zeros between significant digits are significant (for example 1002 has 4 significant digits) A zero after the decimal point is significant when bounded by significant digits to the left (for example 1002.0 has 5 significant digits) Leading zeros are not significant (for example 0.0001 has only one significant digit) All zeroes which are both to the right of the decimal point and to the right of all non-zero significant digits are themselves significant

How many significant digits do these numbers have? 3.14159 Six significant digits (all numbers give you useful information)

How many significant digits do these numbers have? 1000 .0 Five significant digits One significant digit

How many significant digits do these numbers have? 0.00035 Two significant digits Three significant digits

How many significant digits do these numbers have? 560 .0 . Three significant digits (the decimal point after the zero tells us that the measurement was made to the nearest unit, so the zero is not just a place holder) Four significant digits Two significant digits

Precision When adding or subtract measurements, the solution should always have the same precision as the least precise measurement For example find the perimeter of a triangle with sides of length 3.1 m, 12.02 m, and 7.223 m. Looking at the numbers…I see that the first number, 3.1 m, is only accurate to the tenths place; all the other numbers are accurate to a greater number of decimal places. So my answer will have to be rounded to the tenths place…

So what’s the answer? 22.3 m Find the perimeter of a rectangle with length 10.255 cm and with width 7.1 cm

So what’s the answer? 34.7 cm

Precision When multiplying or dividing, multiply or divide the numbers as usual, but then you would round the answer to the same number of significant digits as the least-accurate number. For example: simplify, and round to the appropriate number of significant digits: 16.235 x 0.217 x 5

What’s the product when I multiply all these numbers together? 16.235 x 0.217 x 5 Note that 5 has only one significant digit, so the final answer will need to rounded to one significant digit. What’s the product when I multiply all these numbers together? 17.614975 Since we can only claim one accurate significant digit I will need to round 17.614975 to what? 20

Your Turn Find the product of 0.00435 and 4.6 to the appropriate number of digits. What’s the product? How many significant digits do I need to round to: How do I write my answer? The answer should not be 0.02 because it only has one significant digit. = 0.02001 = Two significant digits = 0.020

Remember For adding/subtracting, use “least accurate place” For multiplying/dividing use “least number of significant digits”

Any Questions??