What is each number written in scientific notation?
2. 1,220,000,000
a. 1.22 x 10
b. 0.122 x 10^10
c. 12.2 x 100^8
d. 1.22 x 10^9
3. 0.0287
a. 0.287 x 10^-1
b. 2.87 x 10^-2
c. 2.87 x 10
d. 28.7 x 100^-3
2. 1,220,000,000
d. 1.22 x 10^9
3. 0.0287
b. 2.87 x 10^-2
You know, numbers in scientific notation are like the cool kids at a party. So much shorter and easier to write!
2. 1,220,000,000 can be written in scientific notation as:
d. 1.22 x 10^9
3. 0.0287 can be written in scientific notation as:
b. 2.87 x 10^-2
To convert a number to scientific notation, we need to express it as a product of a decimal number between 1 and 10 (inclusive) and a power of 10.
Let's break down the options for each number:
2. 1,220,000,000
a. 1.22 x 10
b. 0.122 x 10^10
c. 12.2 x 100^8
d. 1.22 x 10^9
To determine the correct answer, we need to move the decimal point in the original number so that we have a number between 1 and 10.
To do this, we can count the number of zeros after the 2 in 1,220,000,000. In this case, there are 9 zeros.
So, we can write 1,220,000,000 as 1.22 x 10^9. Therefore, the correct answer is option d.
Now let's move on to the second number:
3. 0.0287
a. 0.287 x 10^-1
b. 2.87 x 10^-2
c. 2.87 x 10
d. 28.7 x 100^-3
To convert 0.0287 to scientific notation, we need to move the decimal point to the right until we have a number between 1 and 10.
In this case, we need to move the decimal point three places to the right, resulting in 2.87.
Since we moved the decimal point to the right, the exponent should be negative. In this case, it's -2.
So, we can write 0.0287 as 2.87 x 10^-2. Therefore, the correct answer is option b.
To summarize:
2. 1,220,000,000 is written in scientific notation as 1.22 x 10^9 (option d).
3. 0.0287 is written in scientific notation as 2.87 x 10^-2 (option b).
In scientific notation, you must have a single digit from 1 to 9 followed by some decimal
then multiplying by a power of base 10
for #2, that would rule out b) and c) immediately
clearly 1.22 x 10 = 12.2 , so a) is out also, ....
#3
0.0287 is a small number less than 1, so we expect of power of 10 to have a negative exponent,
ruling out c)
Using the other rule I stated above, what do you think?