Significant Digits By Michelle Lamary and and Caitlin Ostrowski.

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Presentation transcript:

Significant Digits By Michelle Lamary and and Caitlin Ostrowski

Counting Significant Digit Rules 1. All non-zero digits are significant (725, 2, 12) 2. Trapped zeros are significant (101, 2003) 3. Ending zeros are significant only if the decimal point can be seen (100., 1.10, 100, 20) 4. Leading (beginning) zeros are never significant (0.001, 0.9)

Example

Example 1 - Answer Rule 1 – 4 sig digs non-zero digits Rule 1 – 4 sig digs non-zero digits

Example 1 - Answer Rule 1 – 4 sig digs non-zero digits Rule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zeros Rule 2 – 4 sig digs trapped zeros

Example 1 - Answer Rule 1 – 4 sig digs non-zero digits Rule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zeros Rule 2 – 4 sig digs trapped zeros Rule 3 – 2 ending zeros Rule 3 – 2 ending zeros

Example 1 - Answer Rule 1 – 4 sig digs non-zero digits Rule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zeros Rule 2 – 4 sig digs trapped zeros Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 3 – 2 sig digs ending zeros with decimal point shown

Example 1 - Answer Rule 1 – 4 sig digs non-zero digits Rule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zeros Rule 2 – 4 sig digs trapped zeros Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 4 – 0 beginning zeros Rule 4 – 0 beginning zeros

Example 1 - Answer Rule 1 – 4 sig digs non-zero digits Rule 1 – 4 sig digs non-zero digits Rule 2 – 4 sig digs trapped zeros Rule 2 – 4 sig digs trapped zeros Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 4 – 0 beginning zeros Rule 4 – 0 beginning zeros 10 Significant Digits 10 Significant Digits

Example

Example 2 - Answer Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers

Example 2 - Answer Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zero Rule 2 – 1 sig dig trapped zero

Example 2 - Answer Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zero Rule 2 – 1 sig dig trapped zero Rule 3 – 1 ending zero Rule 3 – 1 ending zero

Example 2 - Answer Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zero Rule 2 – 1 sig dig trapped zero Rule 3 – 1 sig dig ending zero with decimal point is shown Rule 3 – 1 sig dig ending zero with decimal point is shown

Example 2 - Answer Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zero Rule 2 – 1 sig dig trapped zero Rule 3 – 1 sig dig ending zero with decimal point is shown Rule 3 – 1 sig dig ending zero with decimal point is shown Rule 4 – beginning zeros are not significant (3 beginning zeros) Rule 4 – beginning zeros are not significant (3 beginning zeros)

Example 2 - Answer Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 1 sig dig trapped zero Rule 2 – 1 sig dig trapped zero Rule 3 – 1 sig dig ending zero with decimal point is shown Rule 3 – 1 sig dig ending zero with decimal point is shown Rule 4 – beginning zeros are not significant (3 beginning zeros) Rule 4 – beginning zeros are not significant (3 beginning zeros) 4 significant digits 4 significant digits

Example

Example 3 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number

Example 3 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zeros Rule 2 – 0 sig dig trapped zeros

Example 3 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zeros Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 ending zeros Rule 3 – 2 ending zeros

Example 3 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zeros Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 3 – 2 sig digs ending zeros with decimal point shown

Example 3 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zeros Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 4 – 0 leading zeros Rule 4 – 0 leading zeros

Example 3 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig dig trapped zeros Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 4 – 0 leading zeros Rule 4 – 0 leading zeros 3 significant digits 3 significant digits

Example

Example 4 - Answer Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers

Example 4 - Answer Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros

Example 4 - Answer Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 2 ending zeros Rule 3 – 2 ending zeros

Example 4 - Answer Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs (2 ending zeros but decimal point is NOT shown) Rule 3 – 0 sig digs (2 ending zeros but decimal point is NOT shown)

Example 4 - Answer Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs (2 ending zeros but decimal point is NOT shown) Rule 3 – 0 sig digs (2 ending zeros but decimal point is NOT shown) Rule 4 – 0 beginning zeros Rule 4 – 0 beginning zeros

Example 4 - Answer Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs (2 ending zeros but decimal point is NOT shown) Rule 3 – 0 sig digs (2 ending zeros but decimal point is NOT shown) Rule 4 – 0 beginning zeros Rule 4 – 0 beginning zeros 2 significant digits 2 significant digits

Example

Example 5 - Answer Rule 1 – 2 sig digs non-zero digits Rule 1 – 2 sig digs non-zero digits

Example 5 - Answer Rule 1 – 2 sig digs non-zero digits Rule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zeros Rule 2 – 0 sig dig trapped zeros

Example 5 - Answer Rule 1 – 2 sig digs non-zero digits Rule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zeros Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 ending zeros Rule 3 – 2 ending zeros

Example 5 - Answer Rule 1 – 2 sig digs non-zero digits Rule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zeros Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 3 – 2 sig digs ending zeros with decimal point shown

Example 5 - Answer Rule 1 – 2 sig digs non-zero digits Rule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zeros Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 4 – 0 beginning zeros Rule 4 – 0 beginning zeros

Example 5 - Answer Rule 1 – 2 sig digs non-zero digits Rule 1 – 2 sig digs non-zero digits Rule 2 – 0 sig dig trapped zeros Rule 2 – 0 sig dig trapped zeros Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 3 – 2 sig digs ending zeros with decimal point shown Rule 4 – 0 beginning zeros Rule 4 – 0 beginning zeros 4 significant digits 4 significant digits

Example

Example 6 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number

Example 6 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule sig digs trapped zeros Rule sig digs trapped zeros

Example 6 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule sig digs trapped zeros Rule sig digs trapped zeros Rule 3 – 0 sig digs ending zeros Rule 3 – 0 sig digs ending zeros

Example 6 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule sig digs trapped zeros Rule sig digs trapped zeros Rule 3 – 0 sig digs ending zeros (decimal point is shown) Rule 3 – 0 sig digs ending zeros (decimal point is shown)

Example 6 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule sig digs trapped zeros Rule sig digs trapped zeros Rule 3 – 0 sig digs ending zeros Rule 3 – 0 sig digs ending zeros Rule 4 – beginning zeros are not significant (7 non significant beginning zeros) Rule 4 – beginning zeros are not significant (7 non significant beginning zeros)

Example 6 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule sig digs trapped zeros Rule sig digs trapped zeros Rule 3 – 0 sig digs ending zeros Rule 3 – 0 sig digs ending zeros Rule 4 – beginning zeros are not significant (7 non significant beginning zeros) Rule 4 – beginning zeros are not significant (7 non significant beginning zeros) 1 significant digit 1 significant digit

Example

Example 7 - Answer Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers

Example 7 - Answer Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zeros Rule 2 – 4 sig digs trapped zeros

Example 7 - Answer Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zeros Rule 2 – 4 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros Rule 3 – 0 sig digs ending zeros

Example 7 - Answer Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zeros Rule 2 – 4 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros (decimal point NOT shown) Rule 3 – 0 sig digs ending zeros (decimal point NOT shown)

Example 7 - Answer Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zeros Rule 2 – 4 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros (decimal point is NOT shown) Rule 3 – 0 sig digs ending zeros (decimal point is NOT shown) Rule 4 – 0 beginning zeros Rule 4 – 0 beginning zeros

Example 7 - Answer Rule 1 – 2 sig digs non-zero numbers Rule 1 – 2 sig digs non-zero numbers Rule 2 – 4 sig digs trapped zeros Rule 2 – 4 sig digs trapped zeros Rule 3 – 0 sig digs ending zeros Rule 3 – 0 sig digs ending zeros Rule 4 – 0 beginning zeros Rule 4 – 0 beginning zeros 6 significant digits 6 significant digits

Example

Example 8 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number

Example 8 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros

Example 8 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 1 ending zero Rule 3 – 1 ending zero

Example 8 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs ( 1 ending zero, but decimal point is NOT shown) Rule 3 – 0 sig digs ( 1 ending zero, but decimal point is NOT shown)

Example 8 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs ( 1 ending zero, but decimal point is NOT shown) Rule 3 – 0 sig digs ( 1 ending zero, but decimal point is NOT shown) Rule 4 – 0 leading zeros Rule 4 – 0 leading zeros

Example 8 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 sig digs ( 1 ending zero, but decimal point is NOT shown) Rule 3 – 0 sig digs ( 1 ending zero, but decimal point is NOT shown) Rule 4 – 0 leading zeros Rule 4 – 0 leading zeros 1 significant digit 1 significant digit

Example

Example 9 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number

Example 9 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros

Example 9 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 6 ending zeros Rule 3 – 6 ending zeros

Example 9 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 6 sig digs ending zeros with decimal point shown Rule 3 – 6 sig digs ending zeros with decimal point shown

Example 9 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 6 sig digs ending zeros with decimal point shown Rule 3 – 6 sig digs ending zeros with decimal point shown Rule 4 – 0 leading zeros Rule 4 – 0 leading zeros

Example 9 - Answer Rule 1 – 1 sig dig non-zero number Rule 1 – 1 sig dig non-zero number Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 6 sig digs ending zeros with decimal point shown Rule 3 – 6 sig digs ending zeros with decimal point shown Rule 4 – 0 leading zeros Rule 4 – 0 leading zeros 7 significant digits 7 significant digits

Example

Example 10 - Answer Rule 1 – 4 sig digs non-zero numbers Rule 1 – 4 sig digs non-zero numbers

Example 10 - Answer Rule 1 – 4 sig digs non-zero numbers Rule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros

Example 10 - Answer Rule 1 – 4 sig digs non-zero numbers Rule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 ending zeros Rule 3 – 0 ending zeros

Example 10 - Answer Rule 1 – 4 sig digs non-zero numbers Rule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 ending zeros (Decimal point is NOT shown) Rule 3 – 0 ending zeros (Decimal point is NOT shown)

Example 10 - Answer Rule 1 – 4 sig digs non-zero numbers Rule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 ending zeros Rule 3 – 0 ending zeros Rule 4 – 0 leading zeros Rule 4 – 0 leading zeros

Example 10 - Answer Rule 1 – 4 sig digs non-zero numbers Rule 1 – 4 sig digs non-zero numbers Rule 2 – 0 sig digs trapped zeros Rule 2 – 0 sig digs trapped zeros Rule 3 – 0 ending zeros Rule 3 – 0 ending zeros Rule 4 – 0 leading zeros Rule 4 – 0 leading zeros 4 significant digits 4 significant digits

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