Indicate if the zeros are significant in each of the following me...

Question

Indicate if the zeros are significant in each of the following measurements:

a. 20.05 °C
b. 5.00 m
c. 0.000 02 g
d. 120 000 yr
e. 8.05 x 10² L

Accepted Answer

Welcome back, everyone. We need to underline the nonsignificant zeros in each of the following measurements. If all zeros are significant, we need to write none. So in our first example, a we have the measurement 108,600 liters. Let's begin by recalling that when we have zeros between significant numbers, they will be significant. Whereas if we have zero that trail with no decimal point, they're going to be insignificant or nonsignificant. So looking at choice a or rather example, a, we would understand that the, between our one and eight, we have a zero and this zero, we won't underline because it will be significant since it's between our significant digits one and eight. However, our significant digit six in this measurement is followed by two trailing zeros which we want to underline because we see that these two trailing zeros are not followed by a decimal point. And so these are going to be nonsignificant. So now let's move on to example, B where we're given the measurement 4.08 times 10 to the fourth power kilograms. Our next rule we want to recall is that when it comes to scientific notation, we consider the base only in this case, our base is going to be 4.08. So let's write that down, we have our base as 4.08. And as we stated before, zeros between significant numbers will be significant. So because we have two significant numbers here, four and an eight and a zero between these two significant numbers, this zero will actually be significant. So because we have a significant, we will not underline any. Since we have a significant zero, we will not underline any of the integers or zeros in this number. And so for B, we will say our answer is none. So now moving on to example, C we have the measurement 20.00 g given. So the next rule we want to recall is that trailing zeros in a number with a decimal point are significant. So looking at our measurement, we would consider our, in the beginning of our measurement two and zero and then the decimal as being our first two significant figures. And then after that decimal, we have two zeros which follow or trail. And so these two zeros will also be significant because as an entirety, this measurement contains a decimal. And so we would say that our answer, for example, C is going to be none because all zeros are significant. So now moving on to example, D we have the measurement 351.6 Kelvin. So looking at the only zero here, we have a one, a decimal place followed by a zero and then followed by a six, as we stated before, when we have zeros between two significant digits, it will be a significant zero. And so therefore, for example, D we also would say our answer is none because all of the integers and all of the zero or the only zero present here is significant. And lastly, we have example, e which gives us our measurement 40 millionths of a meter or 0.40 m. So let's recall our last rule where leading zeros are not significant. And so because we are led with a total of one, we have our decimal .234 and five leading zeros, we will underline each of these zeros including the one before the decimal point. And these will all be nonsignificant. Whereas the four and the zero that end, this measurement will be significant because again, the zero followed by that four or sorry, preceded by the four is going to be significant since again, it's sandwiched right before a significant number being our value for here. And so for our final answer we outlined or we underlined a total of five of our zeros in the measurement given. And so these will be our answers as nonsignificant zeros. So all of our answers beginning with example, A is that the two last zeros in our measurement 108,600 are nonsignificant. So we underline those two zeros. And example, B for our measurement four point oh eight times 10 to the fourth power kilograms, we determined that all digits are significant. So our answer was none in choice. Or example, C we have the measurement 20.00 g in which we found that all of the zeros were significant. So our answer was none. And then in example, D we have the measurement 351.6 Kelvin, where we found that all zeros were significant. So our answer was none. We did not underline any nonsignificant zeros. And then in example, e we had the measurement 40 millionths of a meter in which we found that the first five zeros including the one between decimal places, our only decimal place were all nonsignificant. And so we underlined those zeros. And that will complete this example as all of our final answers. I hope that this made sense. And let us know if you have any questions.

Indicate if the zeros are significant in each of the following measurements: a. 20.05 °C b. 5.00 m c. 0.000 02 g d. 120 000 yr e. 8.05 x 10² L

Key Concepts

Significant Figures

Leading Zeros

Trailing Zeros

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