Question

4 steps for determining the number of digits in a number such as 25¹⁰×8⁶

A) Add, subtract, multiply, divide.
B) Count the digits, square the result, add 1, divide by 2.
C) Multiply exponents, add 1, multiply by base, add exponents.
D) Sum exponents, multiply by base, add 1, multiply by 2.

Answer 1

Finding the number of digits in a number like 25¹⁰ × 8⁶ involves understanding the properties of exponents, combining powers of 2, and ensuring results are in scientific notation. The correct method is not reflected in the options provided. Instead, we combine like terms with powers of 2, add exponents, and adjust to scientific notation if necessary.

Step-by-step explanation:

To determine the number of digits in a number such as 25¹⁰ × 8⁶, we can use the following steps:

1. Recognize that we can simplify the expression by factoring the bases in terms of powers of 2. Since 25 is 5² and 5 is 2.5, we can rewrite 25 as (2.5)². Furthermore, 2 is part of the base 8, which is 2³. This allows us to simplify the multiplication by combining like terms with powers of 2.
2. Multiply the digit terms in the usual way and add the exponents of the exponential terms. This is based on the rules of multiplication of exponentials.
3. Ensure that the result is in scientific notation, which means that the number should have only one non-zero digit to the left of the decimal. If needed, adjust the decimal place and increase the exponent accordingly.
4. To find the number of digits, you would usually write out the final result or recognize the size of the exponent to estimate the number of digits.

However, none of the options given A, B, C, or D provides a correct set of steps for this particular process.