Question

Express each of the following numbers in exponential notation with correct significant figures:(a) 704

(b) 0.03344

(c) 547.9

(d) 22086

(e) 1000.00

(f) 0.0000000651

(g) 0.007157

Short answer

(a) 7.04 × 10²

(b) 3.344 × 10^-2

(c) 5.479 × 10²

(d) 2.2086 × 10⁴

(e) 1.00000 × 10³

(f) 6.51 × 10^-8

(g) 7.157 × 10^-3

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.

1000.00 can be rounded to have 1 significant figure as 1 × 10³ or it can round up to have 3 significant figures as 1.00×10³ if the number has been measured accurately up to that point.

The rest of the numbers can be round up like the following.

Express numbers in scientific notation

Number of significant figures in numbers given above-

(a) The scientific notation of 704.0 is 7.04 × 10^{2 ,}with 3 significant figures

(b) The scientific notation of 0.03344 is 3.344 × 10^-2,with 4 significant figures

(c) The scientific notation of 0.005479 is 5.479 × 10^2,with 4 significant figures

(d) The scientific notation of 22086 is 2.2086 × 10^4,with 5 significant figures

(e) The scientific notation of 1000 is 1.00000 × 10^3,with 4 significant figures

(f) The scientific notation of 0.0000000651 is 6.51 × 10^-8,with 3 significant figures

(g) The scientific notation of 0.007157 is 7.157 × 10^-3,with 4 significant figures