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------------------------------------------------ Counting Significant Digits When Measurements Are Added or Subtracted

Add or subtract the following measurements. Ensure each answer contains the correct number of significant digits.

[tex]
\[
\begin{aligned}
19.77 \, \text{mL} + 17.827 \, \text{mL} &= \square \, \text{mL} \\
18.80 \, \text{mL} + 3.607 \, \text{mL} &= \square \, \text{mL} \\
19.87 \, \text{mL} - 2.507 \, \text{mL} &= \square \, \text{mL} \\
\end{aligned}
\]
[/tex]

When adding or subtracting measurements, it’s important to consider the number of significant figures, especially with decimal places. Here’s a step-by-step explanation for each operation:

1. Addition: 19.77 mL + 17.827 mL

- First, line up the measurements by their decimal points:

```
19.77
+17.827
```

- Perform the addition:

```
37.597
```

- Since 19.77 has two decimal places, the result should be rounded to two decimal places:

```
37.60 mL
```

2. Addition: 18.80 mL + 3.607 mL

- First, line up the measurements by their decimal points:

```
18.80
+ 3.607
```

- Perform the addition:

```
22.407
```

- Since 18.80 has two decimal places, the result should be rounded to two decimal places:

```
22.41 mL
```

3. Subtraction: 19.87 mL - 2.507 mL

- First, line up the measurements by their decimal points:

```
19.870
- 2.507
```

- Perform the subtraction:

```
17.363
```

- Since 19.87 has two decimal places, the result should be rounded to two decimal places:

```
17.36 mL
```

In summary, the results of the calculations with the correct number of significant figures are:

- [tex]$ 19.77 \, \text{mL} + 17.827 \, \text{mL} = 37.60 \, \text{mL} $[/tex]
- [tex]$ 18.80 \, \text{mL} + 3.607 \, \text{mL} = 22.41 \, \text{mL} $[/tex]
- [tex]$ 19.87 \, \text{mL} - 2.507 \, \text{mL} = 17.36 \, \text{mL} $[/tex]