To compare the numbers [tex]\(0.2 \bigcirc 0.21\)[/tex] and [tex]\(0.17 \bigcirc 0.7\)[/tex], let's analyze each pair of numbers step-by-step:
### Comparing [tex]\(0.2\)[/tex] and [tex]\(0.21\)[/tex]
1. Identify the decimal places:
- [tex]\(0.2\)[/tex] has one decimal place.
- [tex]\(0.21\)[/tex] has two decimal places.
2. Align the decimal places by adding a zero to [tex]\(0.2\)[/tex]:
- [tex]\(0.2\)[/tex] becomes [tex]\(0.20\)[/tex].
3. Compare digit by digit:
- The first decimal place for both numbers is [tex]\(2\)[/tex].
- The second decimal place for [tex]\(0.20\)[/tex] is [tex]\(0\)[/tex] and for [tex]\(0.21\)[/tex] is [tex]\(1\)[/tex].
4. Determine the relationship:
- Since [tex]\(0 < 1\)[/tex], [tex]\(0.20 < 0.21\)[/tex], which implies [tex]\(0.2 < 0.21\)[/tex].
Thus,
[tex]\[
0.2 < 0.21
\][/tex]
### Comparing [tex]\(0.17\)[/tex] and [tex]\(0.7\)[/tex]
1. Identify the decimal places:
- [tex]\(0.17\)[/tex] has two decimal places.
- [tex]\(0.7\)[/tex] has one decimal place.
2. Align the decimal places by adding a zero to [tex]\(0.7\)[/tex]:
- [tex]\(0.7\)[/tex] becomes [tex]\(0.70\)[/tex].
3. Compare digit by digit:
- The first decimal place for [tex]\(0.17\)[/tex] is [tex]\(1\)[/tex] and for [tex]\(0.70\)[/tex] is [tex]\(7\)[/tex].
4. Determine the relationship:
- Since [tex]\(1 < 7\)[/tex], [tex]\(0.17 < 0.70\)[/tex], which implies [tex]\(0.17 < 0.7\)[/tex].
Thus,
[tex]\[
0.17 < 0.7
\][/tex]
### Summary
By comparing the numbers as described:
1. [tex]\(0.2 < 0.21\)[/tex]
2. [tex]\(0.17 < 0.7\)[/tex]
The final comparison results are:
[tex]\[
0.2 < 0.21 \quad \text{and} \quad 0.17 < 0.7
\][/tex]
