Use scientific notation to determine which of these numbers has the greatest value: 654,987,034; 645,897,430; or 546,789,340. Write your answer in scientific notation, expressed to the exact decimal place.
To determine which number has the greatest value, we need to convert the numbers to scientific notation and compare their coefficients.
The first number, 654,987,034, can be written in scientific notation as 6.54987034 × 10^8.
The second number, 645,897,430, can be written in scientific notation as 6.4589743 × 10^8.
The third number, 546,789,340, can be written in scientific notation as 5.4678934 × 10^8.
Comparing the coefficients, we can see that the greatest value is 6.54987034 × 10^8.
To compare these numbers in scientific notation, we need to convert them from standard notation to scientific notation.
1. 654,987,034 = 6.54987034 x 10^8
2. 645,897,430 = 6.4589743 x 10^8
3. 546,789,340 = 5.4678934 x 10^8
Comparing the exponents, we can see that all three numbers have the same power of 10.
To determine which number has the greatest value, we need to compare the coefficients (the values in front of the power of 10).
The coefficients are:
1. 6.54987034
2. 6.4589743
3. 5.4678934
From the coefficients, we can see that the number 6.54987034 has the greatest value.
Therefore, the number 654,987,034 expressed in scientific notation to the exact decimal place is 6.54987034 x 10^8 with the greatest value.
To compare the values of these numbers using scientific notation, we need to rewrite them in scientific notation format.
654,987,034 can be written as 6.54987034 × 10^8.
645,897,430 can be written as 6.45897430 × 10^8.
546,789,340 can be written as 5.46789340 × 10^8.
Next, we compare the coefficients (the numbers before the multiplication symbol) of these scientific notations. The number with the greatest coefficient has the greatest value.
Comparing the coefficients:
6.54987034 > 6.45897430 > 5.46789340
Therefore, the number 654,987,034, written in scientific notation as 6.54987034 × 10^8, has the greatest value.