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

Answer 1

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.

Answer 2

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.