Easton broke a cell sample into 88 batches, each weighing 3, point, 9, times, 10, to the power minus 53.9×10
−5
grams. How much did the original sample weigh? Use scientific notation to express your answer. simplfy
To determine the weight of the original sample, we can multiply the weight of each batch (3.9 * 10^(-5) grams) by the number of batches (88).
Weight of original sample = (3.9 * 10^(-5) grams) * 88
To simplify, we can multiply the numbers and add the exponents of 10:
Weight of original sample = (3.9 * 88) * 10^(-5)
Weight of original sample = 343.2 * 10^(-5)
To express the answer in scientific notation, we can move the decimal point one place to the left and adjust the exponent of 10 accordingly:
Weight of original sample = 34.32 * 10^(-4) grams
Therefore, the original sample weighed 34.32 * 10^(-4) grams.
To find the weight of the original sample, we need to multiply the weight of each batch by the total number of batches.
Weight of each batch: 3.9 x 10^(-53.9x10^-5) grams
Total number of batches: 88
To simplify the calculation, let's work with the exponent first.
53.9x10^-5 = (5.39 x 10^1) x (10^-5) = 5.39 x 10^(-4)
Now, we can calculate the weight of each batch.
Weight of each batch = 3.9 x 10^(-5.39 x 10^(-4)) grams
To multiply the weights of each batch by the total number of batches, we can add the exponents:
(3.9 x 10^(-5.39 x 10^(-4))) x (88 x 10^0) grams = 3.9 x 88 x 10^((-5.39 x 10^(-4)) + 0) grams
= 343.2 x 10^(-5.39 x 10^(-4)) grams
To simplify the exponent, we can multiply 5.39 by 10^(-4) and represent it in scientific notation:
5.39 x 10^(-4) = 0.539 x 10^(-3) = 5.39 x 10^(-4+(-4))
= 5.39 x 10^(-8)
Now, we can substitute the simplified exponent back into the weight calculation:
343.2 x 10^(-5.39 x 10^(-4)) grams = 343.2 x 10^(-8) grams
Finally, we can express the weight of the original sample in scientific notation:
= 3.432 x 10^2 x 10^(-8) grams
= 3.432 x 10^(-6) grams
Therefore, the weight of the original sample is 3.432 x 10^(-6) grams.
To find the weight of the original sample, you can multiply the weight of each batch by the number of batches.
Given:
Number of batches (n) = 88
Weight of each batch (w) = 3.9 × 10^-5 grams
To simplify scientific notation calculations, we can first express the weight of each batch in scientific notation by moving the decimal point to the left until there is only one non-zero digit to the left of the decimal point.
3.9 × 10^-5 grams can be expressed as 3.9 × (10^-5) grams.
Now we can calculate the weight of the original sample:
Weight of original sample = Number of batches × Weight of each batch
Weight of original sample = 88 × (3.9 × (10^-5))
To simplify, we can first multiply the constant numbers:
Weight of original sample = 88 × 3.9 × 10^-5
Now multiply 88 and 3.9:
Weight of original sample = 343.2 × 10^-5
To multiply, add the exponents of 10:
Weight of original sample = 3.432 × 10^-3
Therefore, the original sample weighed 3.432 × 10^-3 grams.