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Perform the following calculations and report each answer with the correct number of significant figures.

(a) 62.8 脳 34

(b) 0.147 + 0.0066 + 0.012

(c) 38 脳 95 脳 1.792

(d) 15 鈥 0.15 鈥 0.6155

(e) 8.78 脳 (0.0500/ 0.478)

(f) 140 + 7.68 + 0.014

(g) 28.7 鈥 0.0483

(h) (88.5 鈭 87.57)/ 45.13

Short Answer

Expert verified

(a) 2135.2 = 2100

(b) 0.1656 =0.17

(c) 6469.13 = 6500

(d) 14.2345 = 14

(d) 0.918 = 0.92

(e) 147.694 = 148

(f) 28.6517 = 28.7

(g) 0.020607 = 0.02

Step by step solution

01

Rules to determine the significant figures in a number:

(a) Non-zero digits are usually important.

(b) Any zeros between the first and second significant digits are significant.

(c) Only the last zero or trailing zeros in the decimal section are significant.

(d) Leading zeros, i.e., zeros which come before the decimal point and any non-zero digit, are insignificant

02

Definition of significant figure:

Significant figure is the number of significant single digits in the coefficient of an expression, referred to the accuracy of measurement. The number of significant figures in a statement shows the degree of certainty or precision with which an engineer or scientist states a number.

03

Rules regarding rounding off:

If a rounding number is followed by 5,6,7,8,9, then the number needs to be round up. If a rounding number is followed by 0,1,2,3,4, then the number needs to be round down.

04

Calculation:

\(\begin{array}{c}62.8 \times 34\\ = 2135.2\\0.147 + 0.0066 + 0.012\\ = 0.1656\end{array}\)

\(\begin{array}{c}38 \times 95 \times 1.792\\ = 6469.13\\15 - 0.15 - 0.6155\\ = 14.2345\end{array}\)

\(\begin{array}{l}8.78 \times \frac{{0.0500}}{{0.478}}\\ = 0.918\\140 + 7.68 + 0.014\\ = 147.694\end{array}\)

\(\begin{array}{l}28.7 - 0.0483\\ = 28.6517\\\frac{{\left( {88.5 - 87.57} \right)}}{{45.13}}\\ = 0.020607\end{array}\)

05

Rounding off numbers

(a) Rounding off the number 2135.2 up to two significant figures will be 2100.

(b) Rounding off the number 0.1656up to two significant figures will be 0.17.

(c) Rounding off the number 6469.13 up to two significant figures will be 6500.

(d) Rounding off the number 14.2345 up to two significant figures will be 14

(e) Rounding off the number 0.918 up to two significant figures will be 0.92.

(f) Rounding off the number 147.694 up to two significant figures will be 148.

(g) Rounding off the number 28.6517 up to two significant figures will be 28.7

(h) Rounding off the number 0.020607 up to two significant figures will be 0.02.

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