Q45E - Chemistry (OpenStax)

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

Step-by-Step Solution

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 1: 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.

Step 2: 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