Ten tenths make one whole

4.NF.C.64.NF.C.5 · take · grade 4

Archetype: Place-Value Regrouping · step in a 7-type progression

▶ Practice — 10 problems

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. Two bundles of ten tenths give 2 wholes (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

Two wholes and five 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

Ten 0.1s is exactly one whole, because ten tenths make 1.

10 \times 0.1 = 1

Ten copies of one tenth fill up exactly one whole, so the answer is the whole number 1.

Answer: 2.5 and 1

Review

25 tenths should be a little more than 2 wholes (since 20 tenths = 2), and 2.5 fits. 10 tenths is exactly 1 whole. 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 25 in the tenths position = 2.5, and 10 tenths rolls over to 1 in the ones place = 1.

Standards · min grade 4

4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100 — Writing twenty-five 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!