Question

Compute 4.659×104−2.14×104. Round the answer appropriately.
Express your answer as an integer using the proper number of significant figures (e.g. 12300)

Answer 1

Answer: 25,200.

Explanation:

1) Given: 4.659 × 10⁴ - 2.14 × 10⁴

2) You have to deal with significant figures.

Since, the powers are the same (10⁴) you can directly subtract the decimal numbers. But first analyze the significant figures and the number of decimal digits.

3) The number 4.659 × 10⁴ has four significant figures (4, 6, 5, and 9), while the number 2.14 × 10⁴ has three significan figures (2, 1, and 4).

4) When you add or subtract numbers with diferent amount of decimal digits, the result must show the same number of decimal digits as the term with the least number of decimal digits.

5) Before subtracting, you must round all the terms to the least number of decimal digits. So, since 2.14 has two decimal digits and 4.659 has three decimal digits, you shall round 4.659 to 4.66.

6) Now you subtract 4.66 - 2.14 = 2.52

7) Multiply by the power of 10: 2.52 × 10⁴ = 25,200. And that is the answer.

Answer 2

The result is 25200

4.659 minus 2.14 will produce 3 significant number  referring to a number that has the smallest significant number value of 2.14

Further Explanation  

Significant numbers are numbers obtained from the measurement results of exact numbers and the last number estimated  

In scientific notation, all numbers are displayed before the big order is called significant numbers  

the scientific notation can be described as:  

a, ... x 10ⁿ  

a, ... called an significant numbers  or mantissa

10ⁿ is called a big order  

Rules for significant numbers in general:  

• 1. all non-zero numbers are significant numbers

• 2. a zero which is located between two non-zero numbers including a significant number

• 3. all zeros are located in the final row written behind the decimal point include significant number

• 4. zero decimal point is not significant number
•        5. in scientific notation, significant numbers are coefficient

In the question it is known that  

(4,659 × 10⁴) and (2.14 × 10⁴) both have a significant number in a row 4,659 and 2.14 so that it meets the rule of significant numbers   5 which is 4 and 3 significant number  

So 4.659 minus 2.14 will produce 3 significant number  (because we are referring to a number that has the smallest significant number value of 2.14)

So that we do the significant number/coefficient then proceed a big order  

Because it has the same exponent number, then the coefficients can be directly deducted, except if the exponent number is different then it must be converted first

4.659 - 2.14 = 2.519

So the result = 2.519 . 10⁴

Because the result must have 3 significant number , the result is 25200 (2 zeros behind is not a significant number)

Learn more  

significant figures  

brainly.com/question/11151926  

significant figures in the following number: 5.67 x 106  

brainly.com/question/7539478  

the number of significant figures is 0.025  

brainly.com/question/10343704  

0.080 significant figures  

brainly.com/question/1999241  

the fewest number of significant figures  

brainly.com/question/11464470  

Keywords : significant number, scientific notation, the exponent number