To determine which turtle is hibernating deeper, we'll compare their depths, converted to decimal form.
Start with the box turtle's depth:
1. The box turtle hibernates at [tex]\( -1 \frac{5}{8} \)[/tex] feet.
2. Convert the mixed fraction [tex]\( \frac{5}{8} \)[/tex] to a decimal.
- [tex]\( \frac{5}{8} = 0.625 \)[/tex]
3. Thus, [tex]\( -1 \frac{5}{8} = -1 - 0.625 = -1.625 \)[/tex]
Next, consider the spotted turtle's depth:
1. The spotted turtle hibernates at [tex]\( -1 \frac{16}{25} \)[/tex] feet.
2. Convert the mixed fraction [tex]\( \frac{16}{25} \)[/tex] to a decimal.
- [tex]\( \frac{16}{25} = 0.64 \)[/tex]
3. Thus, [tex]\( -1 \frac{16}{25} = -1 - 0.64 = -1.64 \)[/tex]
Now, let's place these values on a number line:
-1.64 is to the left of -1.625 (since more negative values are situated to the left on a vertical number line).
Comparing [tex]\( -1.625 \)[/tex] and [tex]\( -1.64 \)[/tex]:
- [tex]\( -1.64 < -1.625 \)[/tex]
This means the spotted turtle is hibernating deeper than the box turtle because [tex]\( -1.64 \)[/tex] is further down the vertical number line than [tex]\( -1.625 \)[/tex].
Thus, the spotted turtle is deeper.
