How many digits are there in the Hindu-Arabic form of $$ 5560 \cdot 10^{17} ? $$

Question

UpStudy AI · Accepted Answer

To determine the number of digits in the Hindu-Arabic form of the number $$ 5560 \cdot 10^{17} $$, we can start by rewriting the expression in a more manageable form.

First, we can express $$ 5560 $$ in scientific notation:

$$
5560 = 5.56 \times 10^3
$$

Now, substituting this back into our original expression gives:

$$
5560 \cdot 10^{17} = (5.56 \times 10^3) \cdot 10^{17}
$$

Using the properties of exponents, we can combine the powers of ten:

$$
(5.56 \times 10^3) \cdot 10^{17} = 5.56 \times 10^{3 + 17} = 5.56 \times 10^{20}
$$

Next, we need to convert $$ 5.56 \times 10^{20} $$ into its full decimal form. This involves moving the decimal point in $$ 5.56 $$ twenty places to the right.

Starting with $$ 5.56 $$:

- Moving the decimal point 20 places to the right means we will have $$ 5.56 $$ followed by 20 zeros.
- Since $$ 5.56 $$ has 2 digits before the decimal point, we can write it as:

$$
5.56 \rightarrow 556 \text{ (the digits before the decimal point)} + 20 - 2 = 18 \text{ zeros}
$$

Thus, the full number in decimal form is:

$$
556000000000000000000
$$

Now, we count the digits:

- The digits in $$ 556 $$ contribute 3 digits.
- The 18 zeros contribute 18 digits.

Adding these together gives:

$$
3 + 18 = 21
$$

Therefore, the total number of digits in the Hindu-Arabic form of $$ 5560 \cdot 10^{17} $$ is

$$
\boxed{21}
$$
The Hindu-Arabic form of $$ 5560 \cdot 10^{17} $$ has 21 digits.

How many digits are there in the Hindu-Arabic form of \( 5560 \cdot 10^{17} ? \)

Real Tutor Solution

Answer

Solution

Mind Expander

Related Questions

Latest Arithmetic Questions