what is the sum of 6.3 times 10^3 and 2.41 time 10^4? use scientific notation to express your answer
To find the sum of (6.3 × 10^3) and (2.41 × 10^4), we can add the numbers in front of the powers of 10 separately and keep the power of 10 the same.
First, let's add the numbers in front of the powers of 10:
6.3 + 2.41 = 8.71
Next, we keep the power of 10 the same, which is 10^4.
Therefore, the sum is 8.71 × 10^4.
So, the sum of (6.3 × 10^3) and (2.41 × 10^4) expressed in scientific notation is 8.71 × 10^4.
To find the sum of two numbers in scientific notation, we need to ensure that both numbers have the same exponent.
6.3 times 10^3 can be expressed as 6.3 x 10^3
2.41 times 10^4 can be expressed as 0.241 x 10^5
Now, let's add the two numbers:
6.3 x 10^3 + 0.241 x 10^5 = 6.3 x 10^3 + 0.241 x 10^3 x 10^2 = 6.3 x 10^3 + 0.241 x 10^3 x 100
Simplifying further:
6.3 x 10^3 + 0.241 x 10^3 x 100 = 6.3 x 10^3 + 24.1 x 10^3
Combining like terms:
6.3 x 10^3 + 24.1 x 10^3 = (6.3 + 24.1) x 10^3 = 30.4 x 10^3
Finally, expressing the answer in scientific notation:
30.4 x 10^3 = 3.04 x 10^4
Therefore, the sum of 6.3 times 10^3 and 2.41 times 10^4 is 3.04 x 10^4.
To find the sum of two numbers in scientific notation, we need to compare the exponents and adjust accordingly before performing the addition. Let's break it down step by step.
First, let's rewrite both numbers in scientific notation:
6.3 times 10^3 = 6.3 × 10^3
2.41 times 10^4 = 2.41 × 10^4
Next, we need to match the exponents. In this case, the first number has an exponent of 3, while the second number has an exponent of 4. To align the exponents, we can move the decimal point one place to the right in the first number.
6.3 × 10^3 becomes 63 × 10^2
Now that the exponents are the same, we can add the numbers together:
63 × 10^2 + 2.41 × 10^4 = 63 × 10^2 + 24.1 × 10^3
Since both terms have the same base (10), we can add the coefficients:
63 + 24.1 = 87.1
Therefore, the sum of 6.3 times 10^3 and 2.41 times 10^4 is 87.1 × 10^3 in scientific notation.
Note: In scientific notation, we express the number with one digit before the decimal point, so we need to move the decimal place one position to the left:
87.1 × 10^3 = 8.71 × 10^4.
Therefore, the sum is 8.71 × 10^4.