← 3-1 · Ten tenths make one whole · Place-Value Regrouping

Ten tenths make one whole · 10 practice problems

4.NF.C.64.NF.C.5

Generated variants — 10

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 answer: 2.4 and 5

Write each number described by the conditions below as a decimal.

the number made of twenty-four 0.1s, and the number that is 50 times 0.1

Show solution

Understand

We must write two decimals: (1) the number made of twenty-four 0.1s, and (2) the number that is 50 times 0.1.

Givens

0.1 is one tenth, the unit in the tenths place
The first number is twenty-four copies of 0.1
The second number is 50 times 0.1

Unknowns

The decimal equal to twenty-four 0.1s
The decimal equal to 50 times 0.1

Constraints

Each answer is written in decimal notation
Ten 0.1s regroup into 1 whole

Plan

#5 Look for a Pattern · also uses: #9 Solve an Easier Related Problem

Counting tenths follows the place-value pattern that every 10 tenths bundle into one whole. Starting from the easy fact that ten 0.1s make 1, we extend the pattern to 24 tenths and confirm the second number directly.

Execute

#9 Solve an Easier Related Problem 4.NF.C.6

Group twenty-four 0.1s into bundles of ten. 2 bundle(s) of ten tenths give 2 whole(s) (2.0), and 4 tenths are left over, which is 0.4.

24 \times 0.1 = 20 \times 0.1 + 4 \times 0.1 = 2 + 0.4 = 2.4

Tenths bundle into wholes exactly the way ones bundle into tens, so 24 tenths is 2 wholes and 4 tenths.

#5 Look for a Pattern 4.NF.C.6

2 whole(s) and 4 tenths is written as 2.4.

24 \times 0.1 = 2.4

The digit before the point counts wholes; the digit after counts tenths.

#5 Look for a Pattern 4.NF.C.5

50 0.1s is exactly 5, because every ten tenths make 1.

50 \times 0.1 = 5

Each group of ten copies of one tenth fills up exactly one whole, so 50 tenths is the number 5.

Answer: 2.4 and 5

Review

24 tenths should be near 2 wholes (since 20 tenths = 2), and 2.4 fits. 50 tenths is 5. Both magnitudes match the meaning of a tenth.

Use place value directly (tool 15): 0.1 means 1 in the tenths place, so 24 tenths is 2.4, and 50 tenths is 5.

Standards · min grade 4

4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100 — Writing 24 tenths as the decimal 2.4
4.NF.C.5 Express a fraction with denominator 10 as equivalent with denominator 100 — Recognizing that ten tenths equal one whole

💡 Every ten tenths bundle into one whole, so counting 0.1s is just like counting place values you already know!

Variant 2 answer: 2.5 and 1

Write each number described by the conditions below as a decimal.

the number made of twenty-five 0.1s, and the number that is 10 times 0.1

Show solution

Understand

We must write two decimals: (1) the number made of twenty-five 0.1s, and (2) the number that is 10 times 0.1.

Givens

0.1 is one tenth, the unit in the tenths place
The first number is twenty-five copies of 0.1
The second number is 10 times 0.1

Unknowns

The decimal equal to twenty-five 0.1s
The decimal equal to 10 times 0.1

Constraints

Each answer is written in decimal notation
Ten 0.1s regroup into 1 whole

Plan

#5 Look for a Pattern · also uses: #9 Solve an Easier Related Problem

Counting tenths follows the place-value pattern that every 10 tenths bundle into one whole. Starting from the easy fact that ten 0.1s make 1, we extend the pattern to 25 tenths and confirm the second number directly.

Execute

#9 Solve an Easier Related Problem 4.NF.C.6

Group twenty-five 0.1s into bundles of ten. 2 bundle(s) of ten tenths give 2 whole(s) (2.0), and 5 tenths are left over, which is 0.5.

25 \times 0.1 = 20 \times 0.1 + 5 \times 0.1 = 2 + 0.5 = 2.5

Tenths bundle into wholes exactly the way ones bundle into tens, so 25 tenths is 2 wholes and 5 tenths.

#5 Look for a Pattern 4.NF.C.6

2 whole(s) and 5 tenths is written as 2.5.

25 \times 0.1 = 2.5

The digit before the point counts wholes; the digit after counts tenths.

#5 Look for a Pattern 4.NF.C.5

10 0.1s is exactly 1, because every ten tenths make 1.

10 \times 0.1 = 1

Each group of ten copies of one tenth fills up exactly one whole, so 10 tenths is the number 1.

Answer: 2.5 and 1

Review

25 tenths should be near 2 wholes (since 20 tenths = 2), and 2.5 fits. 10 tenths is 1. Both magnitudes match the meaning of a tenth.

Use place value directly (tool 15): 0.1 means 1 in the tenths place, so 25 tenths is 2.5, and 10 tenths is 1.

Standards · min grade 4

4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100 — Writing 25 tenths as the decimal 2.5
4.NF.C.5 Express a fraction with denominator 10 as equivalent with denominator 100 — Recognizing that ten tenths equal one whole

💡 Every ten tenths bundle into one whole, so counting 0.1s is just like counting place values you already know!

Variant 3 answer: 4.2 and 2

Write each number described by the conditions below as a decimal.

the number made of forty-two 0.1s, and the number that is 20 times 0.1

Show solution

Understand

We must write two decimals: (1) the number made of forty-two 0.1s, and (2) the number that is 20 times 0.1.

Givens

0.1 is one tenth, the unit in the tenths place
The first number is forty-two copies of 0.1
The second number is 20 times 0.1

Unknowns

The decimal equal to forty-two 0.1s
The decimal equal to 20 times 0.1

Constraints

Each answer is written in decimal notation
Ten 0.1s regroup into 1 whole

Plan

#5 Look for a Pattern · also uses: #9 Solve an Easier Related Problem

Counting tenths follows the place-value pattern that every 10 tenths bundle into one whole. Starting from the easy fact that ten 0.1s make 1, we extend the pattern to 42 tenths and confirm the second number directly.

Execute

#9 Solve an Easier Related Problem 4.NF.C.6

Group forty-two 0.1s into bundles of ten. 4 bundle(s) of ten tenths give 4 whole(s) (4.0), and 2 tenths are left over, which is 0.2.

42 \times 0.1 = 40 \times 0.1 + 2 \times 0.1 = 4 + 0.2 = 4.2

Tenths bundle into wholes exactly the way ones bundle into tens, so 42 tenths is 4 wholes and 2 tenths.

#5 Look for a Pattern 4.NF.C.6

4 whole(s) and 2 tenths is written as 4.2.

42 \times 0.1 = 4.2

The digit before the point counts wholes; the digit after counts tenths.

#5 Look for a Pattern 4.NF.C.5

20 0.1s is exactly 2, because every ten tenths make 1.

20 \times 0.1 = 2

Each group of ten copies of one tenth fills up exactly one whole, so 20 tenths is the number 2.

Answer: 4.2 and 2

Review

42 tenths should be near 4 wholes (since 40 tenths = 4), and 4.2 fits. 20 tenths is 2. Both magnitudes match the meaning of a tenth.

Use place value directly (tool 15): 0.1 means 1 in the tenths place, so 42 tenths is 4.2, and 20 tenths is 2.

Standards · min grade 4

4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100 — Writing 42 tenths as the decimal 4.2
4.NF.C.5 Express a fraction with denominator 10 as equivalent with denominator 100 — Recognizing that ten tenths equal one whole

💡 Every ten tenths bundle into one whole, so counting 0.1s is just like counting place values you already know!

Variant 4 answer: 3.6 and 1

Write each number described by the conditions below as a decimal.

the number made of thirty-six 0.1s, and the number that is 10 times 0.1

Show solution

Understand

We must write two decimals: (1) the number made of thirty-six 0.1s, and (2) the number that is 10 times 0.1.

Givens

0.1 is one tenth, the unit in the tenths place
The first number is thirty-six copies of 0.1
The second number is 10 times 0.1

Unknowns

The decimal equal to thirty-six 0.1s
The decimal equal to 10 times 0.1

Constraints

Each answer is written in decimal notation
Ten 0.1s regroup into 1 whole

Plan

#5 Look for a Pattern · also uses: #9 Solve an Easier Related Problem

Counting tenths follows the place-value pattern that every 10 tenths bundle into one whole. Starting from the easy fact that ten 0.1s make 1, we extend the pattern to 36 tenths and confirm the second number directly.

Execute

#9 Solve an Easier Related Problem 4.NF.C.6

Group thirty-six 0.1s into bundles of ten. 3 bundle(s) of ten tenths give 3 whole(s) (3.0), and 6 tenths are left over, which is 0.6.

36 \times 0.1 = 30 \times 0.1 + 6 \times 0.1 = 3 + 0.6 = 3.6

Tenths bundle into wholes exactly the way ones bundle into tens, so 36 tenths is 3 wholes and 6 tenths.

#5 Look for a Pattern 4.NF.C.6

3 whole(s) and 6 tenths is written as 3.6.

36 \times 0.1 = 3.6

The digit before the point counts wholes; the digit after counts tenths.

#5 Look for a Pattern 4.NF.C.5

10 0.1s is exactly 1, because every ten tenths make 1.

10 \times 0.1 = 1

Each group of ten copies of one tenth fills up exactly one whole, so 10 tenths is the number 1.

Answer: 3.6 and 1

Review

36 tenths should be near 3 wholes (since 30 tenths = 3), and 3.6 fits. 10 tenths is 1. Both magnitudes match the meaning of a tenth.

Use place value directly (tool 15): 0.1 means 1 in the tenths place, so 36 tenths is 3.6, and 10 tenths is 1.

Standards · min grade 4

4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100 — Writing 36 tenths as the decimal 3.6
4.NF.C.5 Express a fraction with denominator 10 as equivalent with denominator 100 — Recognizing that ten tenths equal one whole

💡 Every ten tenths bundle into one whole, so counting 0.1s is just like counting place values you already know!

Variant 5 answer: 2.3 and 6

Write each number described by the conditions below as a decimal.

the number made of twenty-three 0.1s, and the number that is 60 times 0.1

Show solution

Understand

We must write two decimals: (1) the number made of twenty-three 0.1s, and (2) the number that is 60 times 0.1.

Givens

0.1 is one tenth, the unit in the tenths place
The first number is twenty-three copies of 0.1
The second number is 60 times 0.1

Unknowns

The decimal equal to twenty-three 0.1s
The decimal equal to 60 times 0.1

Constraints

Each answer is written in decimal notation
Ten 0.1s regroup into 1 whole

Plan

#5 Look for a Pattern · also uses: #9 Solve an Easier Related Problem

Counting tenths follows the place-value pattern that every 10 tenths bundle into one whole. Starting from the easy fact that ten 0.1s make 1, we extend the pattern to 23 tenths and confirm the second number directly.

Execute

#9 Solve an Easier Related Problem 4.NF.C.6

Group twenty-three 0.1s into bundles of ten. 2 bundle(s) of ten tenths give 2 whole(s) (2.0), and 3 tenths are left over, which is 0.3.

23 \times 0.1 = 20 \times 0.1 + 3 \times 0.1 = 2 + 0.3 = 2.3

Tenths bundle into wholes exactly the way ones bundle into tens, so 23 tenths is 2 wholes and 3 tenths.

#5 Look for a Pattern 4.NF.C.6

2 whole(s) and 3 tenths is written as 2.3.

23 \times 0.1 = 2.3

The digit before the point counts wholes; the digit after counts tenths.

#5 Look for a Pattern 4.NF.C.5

60 0.1s is exactly 6, because every ten tenths make 1.

60 \times 0.1 = 6

Each group of ten copies of one tenth fills up exactly one whole, so 60 tenths is the number 6.

Answer: 2.3 and 6

Review

23 tenths should be near 2 wholes (since 20 tenths = 2), and 2.3 fits. 60 tenths is 6. Both magnitudes match the meaning of a tenth.

Use place value directly (tool 15): 0.1 means 1 in the tenths place, so 23 tenths is 2.3, and 60 tenths is 6.

Standards · min grade 4

4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100 — Writing 23 tenths as the decimal 2.3
4.NF.C.5 Express a fraction with denominator 10 as equivalent with denominator 100 — Recognizing that ten tenths equal one whole

💡 Every ten tenths bundle into one whole, so counting 0.1s is just like counting place values you already know!

Variant 6 answer: 1.2 and 2

Write each number described by the conditions below as a decimal.

the number made of twelve 0.1s, and the number that is 20 times 0.1

Show solution

Understand

We must write two decimals: (1) the number made of twelve 0.1s, and (2) the number that is 20 times 0.1.

Givens

0.1 is one tenth, the unit in the tenths place
The first number is twelve copies of 0.1
The second number is 20 times 0.1

Unknowns

The decimal equal to twelve 0.1s
The decimal equal to 20 times 0.1

Constraints

Each answer is written in decimal notation
Ten 0.1s regroup into 1 whole

Plan

#5 Look for a Pattern · also uses: #9 Solve an Easier Related Problem

Counting tenths follows the place-value pattern that every 10 tenths bundle into one whole. Starting from the easy fact that ten 0.1s make 1, we extend the pattern to 12 tenths and confirm the second number directly.

Execute

#9 Solve an Easier Related Problem 4.NF.C.6

Group twelve 0.1s into bundles of ten. 1 bundle(s) of ten tenths give 1 whole(s) (1.0), and 2 tenths are left over, which is 0.2.

12 \times 0.1 = 10 \times 0.1 + 2 \times 0.1 = 1 + 0.2 = 1.2

Tenths bundle into wholes exactly the way ones bundle into tens, so 12 tenths is 1 wholes and 2 tenths.

#5 Look for a Pattern 4.NF.C.6

1 whole(s) and 2 tenths is written as 1.2.

12 \times 0.1 = 1.2

The digit before the point counts wholes; the digit after counts tenths.

#5 Look for a Pattern 4.NF.C.5

20 0.1s is exactly 2, because every ten tenths make 1.

20 \times 0.1 = 2

Each group of ten copies of one tenth fills up exactly one whole, so 20 tenths is the number 2.

Answer: 1.2 and 2

Review

12 tenths should be near 1 wholes (since 10 tenths = 1), and 1.2 fits. 20 tenths is 2. Both magnitudes match the meaning of a tenth.

Use place value directly (tool 15): 0.1 means 1 in the tenths place, so 12 tenths is 1.2, and 20 tenths is 2.

Standards · min grade 4

4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100 — Writing 12 tenths as the decimal 1.2
4.NF.C.5 Express a fraction with denominator 10 as equivalent with denominator 100 — Recognizing that ten tenths equal one whole

💡 Every ten tenths bundle into one whole, so counting 0.1s is just like counting place values you already know!

Variant 7 answer: 4.8 and 3

Write each number described by the conditions below as a decimal.

the number made of forty-eight 0.1s, and the number that is 30 times 0.1

Show solution

Understand

We must write two decimals: (1) the number made of forty-eight 0.1s, and (2) the number that is 30 times 0.1.

Givens

0.1 is one tenth, the unit in the tenths place
The first number is forty-eight copies of 0.1
The second number is 30 times 0.1

Unknowns

The decimal equal to forty-eight 0.1s
The decimal equal to 30 times 0.1

Constraints

Each answer is written in decimal notation
Ten 0.1s regroup into 1 whole

Plan

#5 Look for a Pattern · also uses: #9 Solve an Easier Related Problem

Counting tenths follows the place-value pattern that every 10 tenths bundle into one whole. Starting from the easy fact that ten 0.1s make 1, we extend the pattern to 48 tenths and confirm the second number directly.

Execute

#9 Solve an Easier Related Problem 4.NF.C.6

Group forty-eight 0.1s into bundles of ten. 4 bundle(s) of ten tenths give 4 whole(s) (4.0), and 8 tenths are left over, which is 0.8.

48 \times 0.1 = 40 \times 0.1 + 8 \times 0.1 = 4 + 0.8 = 4.8

Tenths bundle into wholes exactly the way ones bundle into tens, so 48 tenths is 4 wholes and 8 tenths.

#5 Look for a Pattern 4.NF.C.6

4 whole(s) and 8 tenths is written as 4.8.

48 \times 0.1 = 4.8

The digit before the point counts wholes; the digit after counts tenths.

#5 Look for a Pattern 4.NF.C.5

30 0.1s is exactly 3, because every ten tenths make 1.

30 \times 0.1 = 3

Each group of ten copies of one tenth fills up exactly one whole, so 30 tenths is the number 3.

Answer: 4.8 and 3

Review

48 tenths should be near 4 wholes (since 40 tenths = 4), and 4.8 fits. 30 tenths is 3. Both magnitudes match the meaning of a tenth.

Use place value directly (tool 15): 0.1 means 1 in the tenths place, so 48 tenths is 4.8, and 30 tenths is 3.

Standards · min grade 4

4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100 — Writing 48 tenths as the decimal 4.8
4.NF.C.5 Express a fraction with denominator 10 as equivalent with denominator 100 — Recognizing that ten tenths equal one whole

💡 Every ten tenths bundle into one whole, so counting 0.1s is just like counting place values you already know!

Variant 8 answer: 3.5 and 1

Write each number described by the conditions below as a decimal.

the number made of thirty-five 0.1s, and the number that is 10 times 0.1

Show solution

Understand

We must write two decimals: (1) the number made of thirty-five 0.1s, and (2) the number that is 10 times 0.1.

Givens

0.1 is one tenth, the unit in the tenths place
The first number is thirty-five copies of 0.1
The second number is 10 times 0.1

Unknowns

The decimal equal to thirty-five 0.1s
The decimal equal to 10 times 0.1

Constraints

Each answer is written in decimal notation
Ten 0.1s regroup into 1 whole

Plan

#5 Look for a Pattern · also uses: #9 Solve an Easier Related Problem

Counting tenths follows the place-value pattern that every 10 tenths bundle into one whole. Starting from the easy fact that ten 0.1s make 1, we extend the pattern to 35 tenths and confirm the second number directly.

Execute

#9 Solve an Easier Related Problem 4.NF.C.6

Group thirty-five 0.1s into bundles of ten. 3 bundle(s) of ten tenths give 3 whole(s) (3.0), and 5 tenths are left over, which is 0.5.

35 \times 0.1 = 30 \times 0.1 + 5 \times 0.1 = 3 + 0.5 = 3.5

Tenths bundle into wholes exactly the way ones bundle into tens, so 35 tenths is 3 wholes and 5 tenths.

#5 Look for a Pattern 4.NF.C.6

3 whole(s) and 5 tenths is written as 3.5.

35 \times 0.1 = 3.5

The digit before the point counts wholes; the digit after counts tenths.

#5 Look for a Pattern 4.NF.C.5

10 0.1s is exactly 1, because every ten tenths make 1.

10 \times 0.1 = 1

Each group of ten copies of one tenth fills up exactly one whole, so 10 tenths is the number 1.

Answer: 3.5 and 1

Review

35 tenths should be near 3 wholes (since 30 tenths = 3), and 3.5 fits. 10 tenths is 1. Both magnitudes match the meaning of a tenth.

Use place value directly (tool 15): 0.1 means 1 in the tenths place, so 35 tenths is 3.5, and 10 tenths is 1.

Standards · min grade 4

4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100 — Writing 35 tenths as the decimal 3.5
4.NF.C.5 Express a fraction with denominator 10 as equivalent with denominator 100 — Recognizing that ten tenths equal one whole

💡 Every ten tenths bundle into one whole, so counting 0.1s is just like counting place values you already know!

Variant 9 answer: 1.6 and 1

Write each number described by the conditions below as a decimal.

the number made of sixteen 0.1s, and the number that is 10 times 0.1

Show solution

Understand

We must write two decimals: (1) the number made of sixteen 0.1s, and (2) the number that is 10 times 0.1.

Givens

0.1 is one tenth, the unit in the tenths place
The first number is sixteen copies of 0.1
The second number is 10 times 0.1

Unknowns

The decimal equal to sixteen 0.1s
The decimal equal to 10 times 0.1

Constraints

Each answer is written in decimal notation
Ten 0.1s regroup into 1 whole

Plan

#5 Look for a Pattern · also uses: #9 Solve an Easier Related Problem

Counting tenths follows the place-value pattern that every 10 tenths bundle into one whole. Starting from the easy fact that ten 0.1s make 1, we extend the pattern to 16 tenths and confirm the second number directly.

Execute

#9 Solve an Easier Related Problem 4.NF.C.6

Group sixteen 0.1s into bundles of ten. 1 bundle(s) of ten tenths give 1 whole(s) (1.0), and 6 tenths are left over, which is 0.6.

16 \times 0.1 = 10 \times 0.1 + 6 \times 0.1 = 1 + 0.6 = 1.6

Tenths bundle into wholes exactly the way ones bundle into tens, so 16 tenths is 1 wholes and 6 tenths.

#5 Look for a Pattern 4.NF.C.6

1 whole(s) and 6 tenths is written as 1.6.

16 \times 0.1 = 1.6

The digit before the point counts wholes; the digit after counts tenths.

#5 Look for a Pattern 4.NF.C.5

10 0.1s is exactly 1, because every ten tenths make 1.

10 \times 0.1 = 1

Each group of ten copies of one tenth fills up exactly one whole, so 10 tenths is the number 1.

Answer: 1.6 and 1

Review

16 tenths should be near 1 wholes (since 10 tenths = 1), and 1.6 fits. 10 tenths is 1. Both magnitudes match the meaning of a tenth.

Use place value directly (tool 15): 0.1 means 1 in the tenths place, so 16 tenths is 1.6, and 10 tenths is 1.

Standards · min grade 4

4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100 — Writing 16 tenths as the decimal 1.6
4.NF.C.5 Express a fraction with denominator 10 as equivalent with denominator 100 — Recognizing that ten tenths equal one whole

💡 Every ten tenths bundle into one whole, so counting 0.1s is just like counting place values you already know!

Variant 10 answer: 2.7 and 4

Write each number described by the conditions below as a decimal.

the number made of twenty-seven 0.1s, and the number that is 40 times 0.1

Show solution

Understand

We must write two decimals: (1) the number made of twenty-seven 0.1s, and (2) the number that is 40 times 0.1.

Givens

0.1 is one tenth, the unit in the tenths place
The first number is twenty-seven copies of 0.1
The second number is 40 times 0.1

Unknowns

The decimal equal to twenty-seven 0.1s
The decimal equal to 40 times 0.1

Constraints

Each answer is written in decimal notation
Ten 0.1s regroup into 1 whole

Plan

#5 Look for a Pattern · also uses: #9 Solve an Easier Related Problem

Counting tenths follows the place-value pattern that every 10 tenths bundle into one whole. Starting from the easy fact that ten 0.1s make 1, we extend the pattern to 27 tenths and confirm the second number directly.

Execute

#9 Solve an Easier Related Problem 4.NF.C.6

Group twenty-seven 0.1s into bundles of ten. 2 bundle(s) of ten tenths give 2 whole(s) (2.0), and 7 tenths are left over, which is 0.7.

27 \times 0.1 = 20 \times 0.1 + 7 \times 0.1 = 2 + 0.7 = 2.7

Tenths bundle into wholes exactly the way ones bundle into tens, so 27 tenths is 2 wholes and 7 tenths.

#5 Look for a Pattern 4.NF.C.6

2 whole(s) and 7 tenths is written as 2.7.

27 \times 0.1 = 2.7

The digit before the point counts wholes; the digit after counts tenths.

#5 Look for a Pattern 4.NF.C.5

40 0.1s is exactly 4, because every ten tenths make 1.

40 \times 0.1 = 4

Each group of ten copies of one tenth fills up exactly one whole, so 40 tenths is the number 4.

Answer: 2.7 and 4

Review

27 tenths should be near 2 wholes (since 20 tenths = 2), and 2.7 fits. 40 tenths is 4. Both magnitudes match the meaning of a tenth.

Use place value directly (tool 15): 0.1 means 1 in the tenths place, so 27 tenths is 2.7, and 40 tenths is 4.

Standards · min grade 4

4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100 — Writing 27 tenths as the decimal 2.7
4.NF.C.5 Express a fraction with denominator 10 as equivalent with denominator 100 — Recognizing that ten tenths equal one whole

💡 Every ten tenths bundle into one whole, so counting 0.1s is just like counting place values you already know!