Question

Express each of the following numbers in scientific notation with correct significant figures:

(a) 711.0

(b) 0.239

(c) 90743

(d) 134.2

(e) 0.05499

(f) 10000.0

(g) 0.000000738592

Short answer

(a) 7.110 × 10²

(b) 2.39 × 10^-1

(c) 9.0743 × 10⁴

(d) 1.342 × 10²

(e) 5.499 × 10^-2

(f) 1.00000× 10^-4

(g) 7.38592 × 10^-7

Step-by-step solution

Significant and non-significant figures

• All non-zero digits are significant.
• Captive zero/zeros present in between non-zero digits are significant.
• Trailing zero, i.e., zeros present to the right of the decimal, are significant.
• Leading zeros, zeros which come before non-zero digits and the decimal, are not significant and only denote the place of the decimal.

Express numbers in scientific notation

Number of significant figures in numbers given above-

(a) The scientific notation of 711.0 is 7.110 × 10² with 4 significant figures.

(b) The scientific notation of 0.239 is 2.39 × 10^-1,with 3 significant figures.

(c) The scientific notation of 90743 is 9.0743 × 10^{4 ,}with 5 significant figures.

(d) The scientific notation of 134.2 is 1.342 × 10^2,with 4 significant figures.

(e) The scientific notation of 0.05499 is 5.499 × 10^-2,with 4 significant figures.

(f) The scientific notation of 10000 is 1.00000 × 10^-4,with 6 significant figures.

(g) The scientific notation of 0.000000738592 is 7.38592 × 10^-7,with 6 significant figures.