Rounding Decimal Places - Rounding numbers to 2dp - Free Printable

Let's solve both Challenge A and Challenge B step by step using the clues provided.

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✔ CHALLENGE A

We are given 8 decimal numbers:

```
0.317 0.764 0.562 0.64
0.598 0.602 0.657 0.547
```

And the clues:

1. My value is between ¼ and ¾
→ ¼ = 0.25, ¾ = 0.75
So the number must be between 0.25 and 0.75 (not including endpoints).

2. I have 3 decimal places.
→ So we can eliminate any number that doesn’t have exactly 3 decimal places.
Let’s check:
- 0.317 → ✔ 3 decimals
- 0.764 → ✔
- 0.562 → ✔
- 0.64 → ✘ only 2 decimals
- 0.598 → ✔
- 0.602 → ✔
- 0.657 → ✔
- 0.547 → ✔

So eliminate 0.64.

Remaining:
`0.317, 0.764, 0.562, 0.598, 0.602, 0.657, 0.547`

3. My nearest tenth is 0.6
→ Rounding to the nearest tenth means looking at the hundredths place.

Let’s round each remaining number to the nearest tenth:

- 0.317 → 0.3 (since 1 < 5) → ✘
- 0.764 → 0.8 → ✘
- 0.562 → 0.6 (since 6 ≥ 5) → ✔
- 0.598 → 0.6 → ✔
- 0.602 → 0.6 → ✔
- 0.657 → 0.7 → ✘
- 0.547 → 0.5 → ✘

So remaining candidates:
`0.562, 0.598, 0.602`

4. If you round me to the nearest hundredth, I round up.
→ This means when rounding to the nearest hundredth (i.e., two decimal places), the thousandths digit is 5 or more, so we round up.

Let's test each:

- 0.562 → thousandths digit = 2 → round down → ✘
- 0.598 → thousandths digit = 8 → round up → ✔
- 0.602 → thousandths digit = 2 → round down → ✘

Only 0.598 rounds up when going to nearest hundredth.

Let’s verify all clues for 0.598:

- Between 0.25 and 0.75? → Yes, 0.598 ∈ (0.25, 0.75) → ✔
- 3 decimal places? → Yes → ✔
- Nearest tenth? → 0.598 → tenths digit is 5, hundredths is 9 → rounds up to 0.6 → ✔
- Round to nearest hundredth? → 0.598 → look at thousandths (8) → round up → 0.60 → yes, it rounds up → ✔

✔ Answer for Challenge A: 0.598

---

✔ CHALLENGE B

Numbers:
```
4.618 3.725 5.128 1.827
7.514 8.227 9.717 5.625
```

Clues:

1. If you round me to the nearest whole, I round up.
→ This means the tenths digit is ≥ 5, so we round up to the next whole number.

2. If you round me to the nearest tenth, I round down.
→ When rounding to nearest tenth, the hundredths digit is < 5, so we round down.

3. If you round me to the nearest hundredth, I round up.
→ The thousandths digit is ≥ 5, so we round up.

4. None of my digits are multiples of 3.
→ Multiples of 3: 0, 3, 6, 9
So no digit in the number can be 0, 3, 6, or 9

Let’s go through each number.

---

#### Test each candidate:

---

1. 4.618

- Digits: 4, 6, 1, 8 → contains 6 → multiple of 3 → ✘

---

2. 3.725

- Digits: 3, 7, 2, 5 → contains 3 → multiple of 3 → ✘

---

3. 5.128

- Digits: 5, 1, 2, 8 → none are 0,3,6,9 → ✔

Now check rounding:

- Round to nearest whole: 5.128 → tenths digit = 1 < 5 → rounds down to 5 → but clue says "rounds up" → ✘

→ Not valid

---

4. 1.827

- Digits: 1, 8, 2, 7 → none are 0,3,6,9 → ✔

Rounding:

- To nearest whole: 1.827 → tenths = 8 ≥ 5 → rounds up to 2 → ✔
- To nearest tenth: 1.827 → hundredths = 2 < 5 → rounds down to 1.8 → ✔
- To nearest hundredth: 1.827 → thousandths = 7 ≥ 5 → rounds up → 1.83 → ✔
- No digit is multiple of 3 → ✔

All clues satisfied! ✔

Let’s keep checking others to make sure.

---

5. 7.514

- Digits: 7, 5, 1, 4 → none are 0,3,6,9 → ✔

Rounding:

- Nearest whole: 7.514 → tenths = 5 → rounds up to 8 → ✔
- Nearest tenth: 7.514 → hundredths = 1 < 5 → rounds down to 7.5 → ✔
- Nearest hundredth: 7.514 → thousandths = 4 < 5 → rounds down → 7.51 → ✘ (should round up)

→ Fails clue 3 → ✘

---

6. 8.227

- Digits: 8, 2, 2, 7 → none are 0,3,6,9 → ✔

Rounding:

- Nearest whole: 8.227 → tenths = 2 < 5 → rounds down → ✘ (should round up)

→ ✘

---

7. 9.717

- Digits: 9, 7, 1, 7 → contains 9 → multiple of 3 → ✘

---

8. 5.625

- Digits: 5, 6, 2, 5 → contains 6 → multiple of 3 → ✘

---

Only 1.827 satisfies all four clues.

✔ Answer for Challenge B: 1.827

---

✔ Final Answers:

- Challenge A: 0.598
- Challenge B: 1.827

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