Why does adding 4.3×10⁸ and 2.5×10⁷ require showing 455?

[adjacent]

Homework Statement

Calculate $(4.3 \times 10^8)+(2.5 \times 10^7)$
Give your answer in standard form
The total marks for the question is 2

Homework Equations

The Attempt at a Solution

The answer is $4.55 \times 10^8$ because that's what my calculator gave. That will score me one mark. I am not sure how to score the other mark. The mark scheme says 1 mark should be given if figures '455' are seen.
What figures 455? I am confused.

 

[Mark44]

Homework Statement

Calculate $(4.3 \times 10^8)+(2.5 \times 10^7)$
Give your answer in standard form
The total marks for the question is 2

Homework Equations

The Attempt at a Solution

The answer is $4.55 \times 10^8$ because that's what my calculator gave. That will score me one mark. I am not sure how to score the other mark. The mark scheme says 1 mark should be given if figures '455' are seen.
What figures 455? I am confused.

How is "standard form" defined? Your answer of $4.55 \times 10^8$ is the exact answer in scientific notation, but it might not be what they're looking for, depending on how they define standard form. Both of the numbers in the problem are given with two significant digitss, so it might be that they're looking for an answer that is rounded to two significant digits.

 

[RUber]

I did a quick search on the web, and there are conflicting definitions of standard form.
Predominately in Britain, standard form means the same as scientific notation, however some sources use standard form as "not expanded" i.e. 123, 000, 000 and not 100,000,000+20,000,000+3,000000.

 

[Ray Vickson]

How is "standard form" defined? Your answer of $4.55 \times 10^8$ is the exact answer in scientific notation, but it might not be what they're looking for, depending on how they define standard form. Both of the numbers in the problem are given with two significant digitss, so it might be that they're looking for an answer that is rounded to two significant digits.

It is not clear how to do that: should it be $4.5 \times 10^8$ or $4.6 \times 10^8$? If the two numbers are $x_1, x_2$ we have
$$4.251 \times 10^8 \leq x_1 \leq 4.349 \times 10^8 \; \text{ and } \; 2.451 \times 10^7 \leq x_2 \leq 2.349 \times 10^7\\<br /> \text{implies } \;\; 4.4961 \times 10^8 \leq x_1 + x_2 \leq 4.6039 \times 10^8$$

 

[Mark44]

It is not clear how to do that: should it be $4.5 \times 10^8$ or $4.6 \times 10^8$? If the two numbers are $x_1, x_2$ we have
$$4.251 \times 10^8 \leq x_1 \leq 4.349 \times 10^8 \; \text{ and } \; 2.451 \times 10^7 \leq x_2 \leq 2.349 \times 10^7\\<br /> \text{implies } \;\; 4.4961 \times 10^8 \leq x_1 + x_2 \leq 4.6039 \times 10^8$$

There are several ways to round, one of which is "round to even." Since we have 4.55 with a '5' in the 2nd decimal place, the choices are to round to 4.5 or 4.6. The "round to even" rule says to round to an even digit, so we would have 4.6 in this case.

As already mentioned, I don't know what is meant by "standard form," and whether this implies that the result should be rounded. If it should be rounded, there are a number of rounding methods. Without further information from @adjacent, it's hard to say what should be done.

 

[Ray Vickson]

There are several ways to round, one of which is "round to even." Since we have 4.55 with a '5' in the 2nd decimal place, the choices are to round to 4.5 or 4.6. The "round to even" rule says to round to an even digit, so we would have 4.6 in this case.

As already mentioned, I don't know what is meant by "standard form," and whether this implies that the result should be rounded. If it should be rounded, there are a number of rounding methods. Without further information from @adjacent, it's hard to say what should be done.

I know there are rounding "rules", but I have never had much faith in them. However, if the OP's book or notes prescribe a method, that is what the OP should do.