Question

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

(a) 628 x 342
(b) (5363 x 102) x (7.4 x 103)
(c) 28.0/13.483
(d) 8119 x 0.000023
(e) 14.98 + 27,340 + 84.7593
(f) 42.7 + 0.259

Answer 1

Mathematics problems involving significant figures have been solved while adhering to the relevant rules for precision in scientific measurements. The answers were adjusted based on the least number of significant figures or decimal places present in the provided numbers.

Step-by-step explanation:

The subject of this question is Mathematics, more specifically it is related to the concept of significant figures which is a key part of precision in scientific measurements and calculations. The grade level for this question is High School.

• (a) 628 x 342 = 214,776 (reported as 2.15 x 105 because 628 has three significant figures and 342 has three significant figures).
• (b) (5.63 x 102) x (7.4 x 103) = 41,662,000 (reported as 4.17 x 107 because 5.63 has three significant figures and 7.4 has two significant figures).
• (c) 28.0 / 13.483 = 2.076 (reported as 2.08 because 28.0 has three significant figures and 13.483 has five significant figures).
• (d) 8119 x 0.000023 = 0.186737 (reported as 0.00019 because 8119 has four significant figures and 0.000023 has two significant figures).
• (e) 14.98 + 27,340 + 84.7593 = 27,439.7393 (reported as 27,440 because the least number of decimal places in the given numbers is zero).
• (f) 42.7 + 0.259 = 42.959 (reported as 43.0 because 42.7 has three significant figures and 0.259 has three significant figures, but the least precise measurement is to the tenth place).

Answer 2

Explanation :

Significant figures : The figures in a number which express the value -the magnitude of a quantity to a specific degree of accuracy is known as significant digits.

The rule apply for the multiplication and division is :

The least number of significant figures in any number of the problem determines the number of significant figures in the answer.

The rule apply for the addition and subtraction is :

The least precise number present after the decimal point determines the number of significant figures in the answer.

(a) 628 × 342

`628* 342=214776=2.15* 10^5`

The correct answer is,
`2.15* 10^5`

(b) (5363 × 102) × (7.4 × 103)

`(5363* 102)*(7.4* 103)=547026* 762.2=(5.47* 10^5)* (7.6* 10^2)=41.572* 10^7=4.2* 10^8`

The correct answer is,
`4.2* 10^8`

(c) 28.0 ÷ 13.483

`(28.0)/(13.483)=2.08`

The correct answer is, 2.08

(d) 8119 × 0.000023

`8119* 0.000023=0.186737=1.9* 10^(-1)`

The correct answer is,
`1.9* 10^(-1)`

(e) 14.98 + 27,340 + 84.7593

`14.98+27340+84.7593=27439.7393=2.744* 10^4`

The correct answer is,
`2.744* 10^4`

(f) 42.7 + 0.259

`42.7+0.259=42.959=43.0=4.30* 10^1`

The correct answer is,
`4.30* 10^1`