Problem
Ten tenths make one whole
We must write two decimals: (1) the number made of twenty-five 0.1s, and (2) the number that is 10 times 0.1.
Fractions
Your answer
Watch out Don't just drop 25 after the decimal point (giving 0.25) - twenty-five tenths regroup into whole ones plus leftover tenths, giving 2.5.
How to solve
Strategy Look for a Pattern — 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.
1STEP 1
Ten tenths make one whole
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 × 0.1 = 20 × 0.1 + 5 × 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.
4.NF.C.6Solve An Easier Related ProblemTwenty-five 0.1s make two wholes and five tenths, the number 2.5.
Why?
Twenty-five tenths is exactly twenty tenths and five tenths put back together, with nothing lost or added.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Why?
Those twenty tenths make exactly two whole ones.
Why?
Ten tenths bundle up into one whole, the same way ten ones bundle into one ten, so each group of ten tenths becomes one whole.
🧱Place-value groupingTen ones make one ten and ten tens make one hundred — each place bundles ten of the last.
Why?
The five tenths left over is the amount we write as 0.5.
Why?
The first place to the right of the point is the tenths place, so a five sitting there counts five tenths.
🧱Place-value groupingTen ones make one ten and ten tens make one hundred — each place bundles ten of the last.
2STEP 2
Write the first decimal
Two wholes and five tenths is written as 2.5.
25 × 0.1 = 2.5
The digit before the point counts wholes; the digit after counts tenths.
4.NF.C.6Look For A Pattern3STEP 3
Ten times 0.1
Ten 0.1s is exactly one whole, because ten tenths make 1.
10 × 0.1 = 1
Ten copies of one tenth fill up exactly one whole, so the answer is the whole number 1.
4.NF.C.5Look For A PatternAnswer
2.5 and 1
25 × 0.1 = 2.5, 10 × 0.1 = 1
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.
Takeaway
Every ten tenths bundle into one whole, so counting 0.1s is just like counting place values you already know!
- Ten tenths make one whole
- Write the first decimal
- Ten times 0.1
Where next?
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