Compare Very Large and Very Small Numbers Quick Check

Question

2 of 5 2 of 5 Items

Question
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?(1 point)
Responses

1.345763334×109
1.345763334 times 10 superscript 9 baseline
12,920,370,000
12,920,370,000
1.2740876635×1010
1.2740876635 times 10 superscript 10 baseline
1.292037×1010

Answer 1

To compare the numbers 12,740,876,635; 1,345,763,334; and 12,920,370,000 using scientific notation, we first convert each number into scientific notation:

1. 12,740,876,635 can be written as: \[ 1.2740876635 \times 10^{10} \]

2. 1,345,763,334 can be written as: \[ 1.345763334 \times 10^{9} \]

3. 12,920,370,000 can be written as: \[ 1.292037 \times 10^{10} \]

Now we compare the scientific notations:

• \( 1.2740876635 \times 10^{10} \) (for 12,740,876,635)
• \( 1.345763334 \times 10^{9} \) (for 1,345,763,334) which is significantly smaller since it is multiplied by \( 10^{9} \)
• \( 1.292037 \times 10^{10} \) (for 12,920,370,000)

To compare the first and third numbers both of which are in \( 10^{10} \):

• \( 1.2740876635 < 1.292037 \) This means \( 12,740,876,635 < 12,920,370,000 \).

Thus, when we compare the values:

• \( 1.345763334 \times 10^{9} \) is obviously the smallest, and since it is in the order of \( 10^{9} \), it confirms its lesser value.
• Between \( 12,740,876,635 \) and \( 12,920,370,000 \), the latter is larger.

Therefore, the number with the greatest value is 12,920,370,000.