It takes 10 years for a $100 monthly bank deposit to amount to $15,528.23 when invested at 5% interest compounded monthly. Round to the nearest place value, then express the amount $15,528.23 in the form of a×10^n

Question

where a
is single digit..

Answer 1

To express the amount $15,528.23 in the form of $a\times {10}^n$, where $a$ is a single digit, we first write the number in scientific notation.

1. Identify the single digit coefficient $a$:

   • The amount is $15,528.23.
   • We can rewrite it as $1.552823\times {10}^4$ because moving the decimal point 4 places to the left makes it become 1.552823.

2. Round $a$ to one significant figure:

   • Rounding $1.552823$ to one significant figure gives us $2$ (since the first digit after 1 is 5, we round up).

3. Determine $n$:

   • From our previous step, we moved the decimal point 4 places to the left, so $n=4$.

Putting it all together, we have: $$15,528.23\approx 2\times {10}^4$$

Thus, the final answer is: $$\boxed{{\displaystyle 2\times {10}^4}}$$