Decimal place value math worksheet for students with problems involving standard form, word form, and comparing decimals.

Let's solve each problem step by step and explain the reasoning.

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1. Kim measured her pet hamster. The measurements were six and thirty-two hundredths of an inch long. What is the hamster’s measurement in standard form?

Understanding the phrase:
- "Six and thirty-two hundredths" means:
- Whole number part: 6
- Decimal part: 32 hundredths = 0.32

So, putting them together:
> 6 + 0.32 = 6.32

✔ Answer: 6.32

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2. Lenard walks 0.034 of a mile to get to and from school each day. What is this number in word form?

We look at the decimal: 0.034

Break it down:
- The last digit (4) is in the thousandths place.
- So, 0.034 = 34 thousandths

Now check the options:

a. Zero point three four → This is just reading digits, not correct word form
b. Thirty four hundredths → That would be 0.34 → Incorrect
c. Thirty four thousands → Grammatically wrong; "thousands" is not correct here
d. Thirty four thousandths → Correct! Because 0.034 = 34/1000

✔ Answer: d. Thirty four thousandths

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3. Cindy rolled the numbers 4, 5, 2, and 8. What is the largest decimal number she can make using these digits?

We want the largest possible decimal number using all four digits exactly once.

To make the largest number:
- Arrange digits in descending order: 8, 5, 4, 2

So, the largest number is:
> 8542

But wait — the question says "decimal number". Does that mean we need a decimal point?

Since it says "using these digits", and doesn't specify placing a decimal point, but asks for a decimal number, we assume it could be a whole number or include decimals.

However, if we are allowed to use a decimal point, we should place it so the number is maximized.

But with no restrictions on where to put the decimal, the largest possible number would be formed by putting the decimal point after the largest digit — but actually, placing the decimal point after the first digit makes the number smaller.

Wait — let's think carefully.

We have digits: 4, 5, 2, 8

We must use all four digits, and create a decimal number.

The largest possible value comes from:
- Putting the largest digits to the left of the decimal point.
- But since it's a decimal number, we can only have one decimal point.

Best strategy: Use all digits, form the largest number possible.

But to maximize, we should not put the decimal point unless needed.

But the question says “decimal number”, which includes whole numbers (since they are a subset of decimals).

But if we interpret strictly as a decimal number meaning it has a decimal point, then we must place it somewhere.

But even so, the largest number you can make with digits 8, 5, 4, 2 is:

> 8542.0 — but that's still just 8542

Alternatively, if we must include a decimal point, we can try:

- 854.2
- 85.42
- 8.542
- etc.

But clearly, 8542 (without decimal) is larger than any of those.

But perhaps the intention is to form a number with a decimal point, using all four digits.

But the most logical interpretation is: use all digits to form the largest possible number, whether it's a whole number or decimal.

But since 8542 is greater than any decimal like 854.2, etc., the largest number is 8542.

But wait — the question says "decimal number".

In math, decimal number often refers to a number with a decimal point, but sometimes it just means a number written in base 10.

Given that, and since we're using digits, and no restriction, the largest number is 8542.

But let’s suppose we must include a decimal point.

Then the largest number would be when we place the decimal point right after the largest digit.

For example: 854.2 — but we could also do 85.42, 8.542, 0.8542, etc.

Clearly, 854.2 is the largest among those.

But can we do 8542.? That's just 8542.

But if we write it as 8542.0, it's still 8542.

So, if we’re allowed to place the decimal point at the end, it’s fine.

But typically, the largest number using digits 8, 5, 4, 2 is 8542.

But maybe the intent is to form a decimal less than 1, but that wouldn’t make sense.

Alternatively, perhaps the question wants us to form the largest possible number using all digits in some order, possibly with a decimal point.

But again, 8542 is larger than any decimal version.

But let's consider: what if we form 8.542 vs 85.42 vs 854.2 vs 8542. — the largest is 8542.

So, 8542 is the answer.

But wait — is 8542 considered a decimal number?

Yes — because all numbers are decimal numbers in base 10.

So, yes.

✔ Answer: 8542

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4. There is a 2 in the tenths place. The digit in the hundredths place is double that of the tenths place, the digit in the thousandths place is half the amount of the tenths place and the digit in the ten thousandths place is 9. What is the number?

Let’s break this down.

We are building a decimal number with several places.

Let’s label the decimal places:

| Ten Thousandths | Thousandths | Hundredths | Tenths | Units |
|------------------|-------------|------------|--------|-------|
| ? | ? | ? | 2 | ? |

We are told:

- Tenths place = 2
- Hundredths place = double the tenths place → 2 × 2 = 4
- Thousandths place = half the amount of the tenths place → 2 ÷ 2 = 1
- Ten thousandths place = 9

So now fill in:

- Ten thousandths: 9
- Thousandths: 1
- Hundredths: 4
- Tenths: 2
- Units: Not specified → probably 0 unless otherwise stated.

So the number is:

> 0.2419

Let’s verify:

- Tenths: 2 → correct
- Hundredths: 4 → double of 2 → correct
- Thousandths: 1 → half of 2 → correct
- Ten thousandths: 9 → given → correct

✔ Answer: 0.2419

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5. Jayelle cut a piece of string 0.4 inches long and Tim cut a piece of string 0.04 inches long. Whose string was longer?

Compare:

- Jayelle: 0.4 inches
- Tim: 0.04 inches

Now compare:

- 0.4 = 4/10 = 40/100
- 0.04 = 4/100

So, 40/100 > 4/100 → 0.4 > 0.04

Therefore, Jayelle's string is longer

✔ Answer: a. Jayelle

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✔ Final Answers:

1. 6.32
2. d. Thirty four thousandths
3. 8542
4. 0.2419
5. a. Jayelle

Let me know if you'd like a printed version or explanation for students!