Compute 4.659×104−2.14×104. Round the answer appropriately.

The final result is 25200

The operation 4.659 minus 2.14 will yield 3 significant figures based on the least number of significant digits in 2.14

Additional insight

Significant figures are derived from measures of exact values and the last digit is estimated

In the realm of scientific notation, all numbers appearing before the large order are considered significant

scientific notation can be represented as:

a,... x 10ⁿ  

a,... is termed the significant figure or mantissa

10ⁿ indicates the large order

Overall rules for significant figures:  

• 1. All non-zero digits are significant numbers

• 2. A zero that appears between two non-zero digits is significant, including as a significant figure

• 3. Any zeros at the end of a number written after the decimal point are significant figures

• 4. A zero without a decimal point is not a significant figure
•        5. In scientific notation, significant figures are the coefficients

For this question, we know that  

So, performing the operation 4.659 minus 2.14 will yield 3 significant digits  (based on the number of significant figures for 2.14 being the lowest)

Thus, we follow through with the significant number/coefficient before applying a large order  

As their exponentes are equal, operations can proceed directly, unless their exponents differ, in which case conversion is necessary.

4.659 - 2.14 = 2.519

Because the final answer requires 3 significant figures, the output is 25200 (the two trailing zeros do not count as significant figures)

Learn more

about significant figures

significant figures depicted in this number: 5.67 x 106  

the number of significant figures in 0.025  

0.080 significant digits  

the least number of significant figures  

Keywords: significant numbers, scientific notation, exponent of a number

Answer: 25,200.

Explanation:

1) Starting with: 4.659 × 10⁴ - 2.14 × 10⁴

2) Significant figures need to be considered.

Because the powers are equal (10⁴), the decimal values can be subtracted directly. However, it is essential to first check significant figures and the count of decimal places.

3) The figure 4.659 × 10⁴ has four significant digits (4, 6, 5, and 9), whereas 2.14 × 10⁴ contains three significant digits (2, 1, and 4).

4) When adding or subtracting values with a different number of decimal places, the answer must reflect the same number of decimal places as the number with the least amount of decimal precision.

5) Prior to performing subtraction, it is necessary to round the numbers to the least decimal places. Given that 2.14 has two decimal places and 4.659 has three, round 4.659 to 4.66.

6) Now perform the subtraction 4.66 - 2.14 = 2.52

7) Then multiply by the power of 10: 2.52 × 10⁴ = 25,200. This is the final answer.