To compare the numbers 654, 987, 034; 645, 897, 430; and 546, 7899, 340 using scientific notation, we'll first convert each number into scientific notation.
-
654,987,034:
- Move the decimal point 8 places to the left
- \( 654,987,034 = 6.54987034 \times 10^8 \)
-
645,897,430:
- Move the decimal point 8 places to the left
- \( 645,897,430 = 6.45897430 \times 10^8 \)
-
546,789,9340:
- Move the decimal point 9 places to the left
- \( 546,789,9340 = 5.467899340 \times 10^9 \)
Now let's compare the values:
-
For 654,987,034:
\[ 6.54987034 \times 10^8 \] -
For 645,897,430:
\[ 6.45897430 \times 10^8 \] -
For 546,789,9340:
\[ 5.467899340 \times 10^9 \]
To determine which has the greatest value, we first observe the powers of 10. The number with the highest power of 10 is the largest.
- The third number \( 5.467899340 \times 10^9 \) has a power of \( 10^9 \), which is greater than the powers of the other two numbers (\( 10^8 \)).
Thus, the number with the greatest value is:
\[ \boxed{5.467899340 \times 10^9} \]