A certain insect is approximately 4x10^-2 inches long. A second insect is about 1.3x10^-1 inches long. What is the total length of the two insects in inches? Use scientific notation to express your answer to 1 decimal place.
To express the length of an insect we should sum up their lengths in scientific notation: 4.0 × 10^-2 + 1.3 × 10^-1 = 1.7 × 10^-1.
The total length is 1.7 × 10^-1 inches. Answer: \boxed{1.7 \times 10^{-1}}.
To find the total length of the two insects, we need to add their lengths together.
The first insect has a length of approximately 4x10^-2 inches.
The second insect has a length of about 1.3x10^-1 inches.
To add these two lengths, we need to make sure that they have the same exponent in their scientific notation.
Converting the first insect's length, 4x10^-2, to have the same exponent as the second insect gives us 4x10^-2 * 10^0. This is because 10^0 = 1, so multiplying by 10^0 does not change the value.
Now we can add the two lengths together:
(4x10^-2 * 10^0) + (1.3x10^-1)
The exponents are the same, so we can add the coefficients (the numbers in front of the powers of 10):
4x10^-2 * 10^0 = 4x10^(-2+0) = 4x10^-2
1.3x10^-1
Adding these two lengths together gives us:
4x10^-2 + 1.3x10^-1 = (4 + 13) x 10^-2 = 17 x 10^-2
To express the answer in scientific notation to 1 decimal place, we need to move the decimal point one place to the left:
17 x 10^-2 = 1.7 x 10^-1
Therefore, the total length of the two insects is approximately 1.7x10^-1 inches.
To find the total length of the two insects, we need to add their lengths together. Let's denote the length of the first insect as A and the length of the second insect as B.
The length of the first insect is given as approximately 4x10^-2 inches. This can be written as A = 4x10^-2 inches.
The length of the second insect is given as about 1.3x10^-1 inches. This can be written as B = 1.3x10^-1 inches.
To add those lengths together, we need to align the exponents. Since both are in scientific notation, this is already done for us.
Adding A and B:
A + B = (4x10^-2) + (1.3x10^-1)
To simplify the addition, we can convert the numbers to a similar power of 10. In this case, we can convert 4x10^-2 to have the same power as 1.3x10^-1.
To do this, we can rewrite 4x10^-2 as 0.4x10^-1 (since multiplying by 10^-1 is equivalent to moving the decimal point one place to the left).
Now we have:
A + B = (0.4x10^-1) + (1.3x10^-1)
Next, we can add the coefficients:
A + B = 0.4 + 1.3
A + B = 1.7
Since the question asks us to express our answer in scientific notation to 1 decimal place, we can write the total length of the two insects as:
A + B = 1.7x10^0 inches
1.7x10^0 can be simplified to just 1.7, so the total length of the two insects is approximately 1.7 inches.