# What is p+q? Please give step by step method.

In this question $p = a\times10^m$ and $q=b\times 10^m$, where $a+b > 10$,

what is $p+q$?

I may be right or wrong, I do not know, but this is what I have so far:

$$p+q > (a+b) \times 10^m$$

Give a step by step method please.

• Wha-ah? What you might have is $p+q = (a+b) \times 10^m > 10^{m+1}$, but your inequality can't be right. Apr 20 '17 at 19:25
• @BrianTung yeah that's probably right. Mine was more of a wild attempt than anything, I really was not sure what to do. Apr 20 '17 at 19:26
• If you change your inequality to an equality then you have what $p+q$ is. (Note however that the question "what is $p+q$" is vague. A question like "what is $p+q$ in terms of $a$ and $b$ would be much clearer)
– Χpẘ
Apr 20 '17 at 19:33
• Are we given $a, b < 10$? Apr 20 '17 at 19:46
• Do an example. Take $a=b=6$, and $m=2$. What's $600+600$? How does that compare with $(6+6)100$? Apr 20 '17 at 20:01

It is perfectly correct to say $p+q=(a+b)\times10^m$, but it will be marked wrong because the unstated assumption is that the thing that isn't a power of $10$ should be between $1$ and $10$. The expected answer is $p+q=\frac {a+b}{10} \times 10^{m+1}$. Assuming $1 \le a,b \lt 10$ and as you are given $a+b \gt 10$ you know the thing multiplying the power of $10$ is between $1$ and $10$.