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Chapter 51: Problem 3

Give the following numbers to the accuracy indicated: (a) \(214.51\) to three significant figures (b) 107029 to three significant figures (c) \(0.0450\) to one significant figure (d) \(99.817\) to two decimal places (e) \(99.897\) to two decimal places (f) \(99.997\) to two decimal places (g) 6255 to the nearest 10 (h) 134903 to the nearest ten thousand State the following: (i) the number of significant figures in 3400 (j) the number of significant figures in \(3400.3\) (k) the number of significant figures in \(0.00167\) (I) the number of significant figures in \(1.00167\) (m) the number of decimal places in \(34.46\) (n) the number of decimal places in \(0.00167\)

Short Answer

Expert verified
a) 215, b) 107000, c) 0.04, d) 99.82, e) 99.90, f) 100.00, g) 6260, h) 130000, i) 2, j) 5, k) 3, l) 6, m) 2, n) 5

Step by step solution

01

Give numbers to the specified accuracy

(a) \(214.51\) to three significant figures is \(215\).\n (b) 107029 to three significant figures is 107000.\n (c) \(0.0450\) to one significant figure is \(0.04\).\n (d) \(99.817\) to two decimal places is \(99.82\).\n (e) \(99.897\) to two decimal places is \(99.90\).\n (f) \(99.997\) to two decimal places is \(100.00\).\n (g) 6255 to the nearest 10 is 6260.\n (h) 134903 to the nearest ten thousand is 130000.
02

State the number of significant figures

(i) the number of significant figures in 3400 is 2 because zeroes following the other figures but before the implied decimal point are not considered significant. (j) the number of significant figures in \(3400.3\) is 5 as the zero before the decimal point is now significant as it is between two other figures.(k) the number of significant figures in \(0.00167\) is 3. None of the zero is considered significant.(l) the number of significant figures in \(1.00167\) is 6 as all zeros are significant.
03

State the number of decimal places

(m) the number of decimal places in \(34.46\) is 2 as there are two digits after the decimal point.(n) the number of decimal places in \(0.00167\) is 5 as there are five digits after the decimal point, including the zeroes.

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