How many digits does the number $3.00435\times 10^9+0.00002 \times 10^{-53}$ have?

Question

How many digits does the number $$3.00435\cdot10^9+0.00002\cdot10^{-53}$$ have? Can anyone help to find this? Thanks

Any thought about this question? – Siong Thye Goh Oct 24 '16 at 15:50 — Siong Thye Goh, Oct 24 '16 at 15:50

score 1 · Answer 1 · answered Oct 24 '16 at 19:00

HINT: Multiplying by $10$ moves the decimal point one place to the right; multiplying by $10^{-1}$ moves it one place to the left. Thus,

$$3.00435\cdot10^9=3004350000$$

and

$$0.00002\cdot10^{-53}=0.\underbrace{00\ldots00}_{53\text{ zeroes}}00002\;.$$

If you think about it for a moment, it’s not hard to count the digits in the sum.

score 0 · Answer 2 · answered Oct 24 '16 at 15:59

0

The first number 3.00435×10^9 has 10 digits. The second number is equal to 2×10^(-58) which has 58 digits. Hence a total of 68 digits.

answered Oct 24 '16 at 15:59

4

By that line of reasoning, I could say "$1$ has one digit, $10$ has two digits, hence $1 + 10$ should have a total of $3$ digits". A bit more explanation is needed here. – Ben Grossmann Oct 24 '16 at 16:01
What I meant was when we add a whole number and a decimal number like the one asked i.e 0.0000...2 where there are 57 zeroes the total no.of digits are 10+58=68 – Oct 24 '16 at 16:03
Then that's what you should say. Giving answers in a precise and clear fashion is hard, but is a part of answering questions – Ben Grossmann Oct 24 '16 at 16:05

2 Answers2