Connect with a community of experts and enthusiasts on IDNLearn.com. Join our interactive Q&A community and get reliable, detailed answers from experienced professionals across a variety of topics.
Sagot :
To solve the problem, we need to find a decimal number between 0.36 and 0.42 using three different digits. Let's break down the steps.
1. Identify the Range:
- The lower bound is [tex]\(\frac{36}{100} = 0.36\)[/tex].
- The upper bound is [tex]\(\frac{42}{100} = 0.42\)[/tex].
2. Three-Digit Decimal:
- The number Alice needs to form is a three-digit decimal in the form [tex]\(0.abc\)[/tex], where [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] are digits from 0 to 9 and none of them are the same.
3. Determine Valid Digits:
- We need to find all combinations of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] such that [tex]\(0.36 < 0.abc < 0.42\)[/tex].
4. Forming and Validating Numbers:
The following are the valid three-digit decimals that Alice could form:
- 0.360
- 0.361
- 0.362
- 0.364
- 0.365
- 0.367
- 0.368
- 0.369
- 0.370
- 0.371
- 0.372
- 0.374
- 0.375
- 0.376
- 0.378
- 0.379
- 0.380
- 0.381
- 0.382
- 0.384
- 0.385
- 0.386
- 0.387
- 0.389
- 0.390
- 0.391
- 0.392
- 0.394
- 0.395
- 0.396
- 0.397
- 0.398
- 0.401
- 0.402
- 0.403
- 0.405
- 0.406
- 0.407
- 0.408
- 0.409
- 0.410
- 0.412
- 0.413
- 0.415
- 0.416
- 0.417
- 0.418
- 0.419
Each of these numbers satisfies the requirement of being between 0.36 and 0.42. Thus, Alice has numerous possible combinations of digits to choose from to form a valid decimal number within the specified range.
1. Identify the Range:
- The lower bound is [tex]\(\frac{36}{100} = 0.36\)[/tex].
- The upper bound is [tex]\(\frac{42}{100} = 0.42\)[/tex].
2. Three-Digit Decimal:
- The number Alice needs to form is a three-digit decimal in the form [tex]\(0.abc\)[/tex], where [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] are digits from 0 to 9 and none of them are the same.
3. Determine Valid Digits:
- We need to find all combinations of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] such that [tex]\(0.36 < 0.abc < 0.42\)[/tex].
4. Forming and Validating Numbers:
The following are the valid three-digit decimals that Alice could form:
- 0.360
- 0.361
- 0.362
- 0.364
- 0.365
- 0.367
- 0.368
- 0.369
- 0.370
- 0.371
- 0.372
- 0.374
- 0.375
- 0.376
- 0.378
- 0.379
- 0.380
- 0.381
- 0.382
- 0.384
- 0.385
- 0.386
- 0.387
- 0.389
- 0.390
- 0.391
- 0.392
- 0.394
- 0.395
- 0.396
- 0.397
- 0.398
- 0.401
- 0.402
- 0.403
- 0.405
- 0.406
- 0.407
- 0.408
- 0.409
- 0.410
- 0.412
- 0.413
- 0.415
- 0.416
- 0.417
- 0.418
- 0.419
Each of these numbers satisfies the requirement of being between 0.36 and 0.42. Thus, Alice has numerous possible combinations of digits to choose from to form a valid decimal number within the specified range.
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your questions are important to us at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.