Question
__ (d) Zeros to the right of a decimal and to the right of a nonzero number (are or are not)significant? (25.00) __ (e) Zeros to the left of an understood decimal and to the right of a nonzero number (are or are not) significant? (1500) __ (f) Zeros to the left of a printed decimal and to the right of a nonzero number (are or are not) significant? (1500.) 7. How many significant digits are in each of the following measurements? __ (a) 83.49 __ (k) 0.005 __ (f) 40,309 __ (b) 11.00 __ (g) 6.0035 __ (1) 0.09 o __ (c) 300 __ (h) 50. __ (m) 505.05 __ (d) .006900 __ (n) 7,500 __ (i) .0000509 __ (e) 36,900 . __ (0) 0.007090 __ (i) 0.00030000 8. Write the number "five hundred" to the given number of significant digits: __ (a) 1 significant digit __ (b) 3 significant digits __ (c) 5 significant digits 9. Round each of the following to the indicated number of significant digits: __ (a) Round 0.00567 to 1 significant digit __ (b) Round 6.09450 to 2 significant digits __ (c) Round 10.0309 to 3 significant digits
Solution
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JohnMaster · Tutor for 5 years
Answer
**(d)** Zeros to the right of a decimal and to the right of a nonzero number **are** significant. (25.00 has four significant figures) These zeros indicate the precision of the measurement.<br /><br />**(e)** Zeros to the left of an *understood* decimal and to the right of a nonzero number **are not** significant. (1500 has two significant figures) These zeros are placeholders. We don't know if the measurement was made to the nearest hundred, ten, or one.<br /><br />**(f)** Zeros to the left of a *printed* decimal and to the right of a nonzero number **are** significant. (1500. has four significant figures) The decimal point indicates that the measurement was made to the nearest one, and the zeros are significant.<br /><br /><br />**7. Significant Digits:**<br /><br />**(a)** 83.49 (4 significant figures)<br />**(b)** 11.00 (4 significant figures)<br />**(c)** 300 (1 significant figure)<br />**(d)** 0.006900 (4 significant figures)<br />**(e)** 36,900. (5 significant figures - note the decimal point)<br />**(f)** 40,309 (5 significant figures)<br />**(g)** 6.0035 (5 significant figures)<br />**(h)** 50. (2 significant figures - the decimal point makes the zero significant)<br />**(i)** 0.0000509 (3 significant figures)<br />**(j)** 0.00030000 (5 significant figures)<br />**(k)** 0.005 (1 significant figure)<br />**(l)** 0.090 (2 significant figures)<br />**(m)** 505.05 (5 significant figures)<br />**(n)** 7,500 (2 significant figures)<br />**(o)** 0.007090 (4 significant figures)<br /><br /><br />**8. "Five Hundred" to Significant Digits:**<br /><br />**(a)** 500 (1 significant figure)<br />**(b)** 5.00 x 10² or 500. (3 significant figures - using scientific notation or a decimal point)<br />**(c)** 500.00 (5 significant figures)<br /><br /><br />**9. Rounding to Significant Digits:**<br /><br />**(a)** Round 0.00567 to 1 significant digit: 0.006<br />**(b)** Round 6.09450 to 2 significant digits: 6.1<br />**(c)** Round 10.0309 to 3 significant digits: 10.0<br />
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