Significant Digits Perhaps the most boring part of learning chemistry

Measuring things It is never possible to measure something exactly There will always be one number in a measurement that is estimated The number of digits in a measurement that are known with certainty PLUS the estimated number are called significant digits

Whether measuring length… What is this measurement? How many significant digits are there?

Whether measuring length… cm 4 significant digits

Or volume… What is this measurement? How many significant digits are there?

Or volume… 6.62 ml Three significant digits

Or mass… What is this measurement? How many significant digits are there?

Or mass… g 5 significant digits

Problems occur when we use these measurements in doing calculations… For example, if we were measuring the side of a cube with our ruler, and each side measured cm, the volume calculated would be cm 3 ! To keep things a bit under control, there are a few rules we must follow…

When multiplying or dividing measurements… The product or quotient can have NO MORE significant digits than the measurement with the least number of significant digits In our previous example with the cube, cm 3 becomes 1577 cm 3, with 4 significant digits.

When adding or subtracting measurements… The sum or difference can have NO MORE places after the decimal point than the measurement with the least number of decimal places If we measured 6.62 ml of liquid with our graduated cylinder, and then 6.6 ml with a cheaper model, the sum of both would be 13.2 ml, with one digit after the decimal place

Rounding off…

When using a calculator to perform functions involving measurements, always know the number of significant digits the result should have… If the number immediately after the last significant digit is greater than or equal to 5, then round the last significant digit up to three significant digits….826 ≥.500, therefore round 125 up to 126

When using a calculator to perform functions involving measurements, always know the number of significant digits the result should have… If the number immediately after the last significant digit is less than 5, then round the last significant digit down to three significant digits….226 ≤.500, therefore leave 125 alone

147.25two sig digs three sig digs 2.055one sig dig 2.055two sig digs 2.055three sig digs one sig dig three sig digs five sig digs Round to the number of significant digits

Zeroes in the beginning of a number never count sig figs More rules…

Zeroes at the end of a number count only if there is a written decimal point sig figs sig figs More rules…

The digits always count sig figs More rules…

Zeroes between the digits always count sig figs More rules…

How many significant digits?

How to PO your dad He sends you down to the store to buy some carpet. He says he measured the room to be 9 feet by 7 feet. You come home with 60 sq. ft. of carpet. He says, “Are you nuts? Can’t you multiply?” You tell him that Mr. Stine taught you all about significant digits and rounding in chemistry class, and that he should have measured more accurately.

Density lab We will measure the mass and dimensions of ten different regular solids We will use Excel to figure the – Volume – Density – Error – Percentage error