Use scientific notation to compare these numbers: 12,740,876,635; 1,345,763,334; and 12,920,370,000, which has the greatest value?
To compare these numbers using scientific notation, we need to express them in the form of 𝑎 × 10^𝑛, where 1 ≤ 𝑎 < 10 and 𝑛 is an integer.
12,740,876,635 can be written as 1.2740876635 × 10^10.
1,345,763,334 can be written as 1.345763334 × 10^9.
12,920,370,000 can be written as 1.292037 × 10^10.
Comparing the exponents, we see that both 12,740,876,635 and 12,920,370,000 are raised to the power of 10.
Comparing the coefficients, we see that 1.292037 > 1.2740876635 > 1.345763334.
Therefore, the number 12,920,370,000 (1.292037 × 10^10) has the greatest value among the given numbers.
To compare these numbers using scientific notation, we need to express them in the form of A × 10^B, where A is a number between 1 and 10, and B is an integer.
Let's express each number in scientific notation:
12,740,876,635 = 1.2740876635 × 10^10
1,345,763,334 = 1.345763334 × 10^9
12,920,370,000 = 1.292037 × 10^10
To compare these numbers, we compare the values of A × 10^B. We can see that the largest value is 1.292037 × 10^10, which corresponds to 12,920,370,000.
Therefore, 12,920,370,000 has the greatest value.
To compare these numbers using scientific notation, we need to express them in a standardized form. Here's how you can do it:
Step 1: Write each number in scientific notation. Scientific notation represents a number as the product of a decimal number between 1 and 10, and a power of 10.
12,740,876,635 can be written as 1.2740876635 x 10^10.
1,345,763,334 can be written as 1.345763334 x 10^9.
12,920,370,000 can be written as 1.292037 x 10^10.
Step 2: Compare the numbers. Since the decimal part (mantissa) of each number is between 1 and 10, we can compare the powers of 10 to determine which number is the greatest.
Both 1.292037 x 10^10 and 1.2740876635 x 10^10 have the same power of 10 (10^10). However, when comparing the mantissas (the decimal parts), we find that 1.292037 is greater than 1.2740876635.
Therefore, out of the given numbers, 12,920,370,000 has the greatest value when expressed in scientific notation.