A Peek Beyond the Point · Lesson 3 of 11
A Hundredth Part
“See how splitting tenths again lets us describe finer measurements.”
• Explain how hundredths arise from dividing each tenth into ten parts. • Relate whole units, tenths, and hundredths. • Express one measurement in several equivalent fractional forms. • Locate and compare measurements using hundredths.
A Hundredth Part
Imagine a paper strip that measures 8 units and 9 tenths. Fold it so its two ends meet and the strip is halved along its length. The folded length lies between 4 units and 4 tenths and 4 units and 5 tenths. Tenths alone cannot name that middle position exactly. We need smaller equal subdivisions.
Split each tenth into ten equal parts. Since a whole unit already contains ten tenths, it now contains 10 × 10 = 100 of these smaller parts. Each small part is one-hundredth of the original unit. The whole has stayed the same; only the measuring parts have become smaller.
One of one hundred equal parts of a unit. It is written as 1/100 of the unit.
The 45 shaded squares in the diagram can be counted as four complete rows of ten and five extra squares. That is four tenths and five hundredths. Counting every square separately gives forty-five hundredths. These are two ways of naming the same shaded amount.
Problem
A strip of length 8 + 9/10 units is folded exactly in half. Describe the folded length using hundredths.
- 1.Convert the original length into hundredths: 8 units = 800 hundredths and 9 tenths = 90 hundredths.
- 2.The strip is 890 hundredths long. Half of 890 is 445.
- 3.Group 445 hundredths into 4 units and 45 hundredths.
- 4.Forty-five hundredths contain 4 tenths and 5 hundredths. The folded length is 4 + 4/10 + 5/100 units.
One Length, Several Names
Changing the grouping can make a measurement easier to read or compare. A wire of length 1 unit, 1 tenth, and 4 hundredths contains a whole unit plus fourteen hundredths. It also contains 114 hundredths altogether. Each description should give the same point on the same measuring scale.
Problem
Write 1 + 1/10 + 4/100 units in two other equivalent forms.
- 1.Replace the tenth with 10 hundredths. The fractional part is 10/100 + 4/100 = 14/100.
- 2.The first equivalent form is 1 + 14/100 units.
- 3.Replace the whole unit with 100 hundredths. The total is 100 + 14 = 114 hundredths.
- 4.The second equivalent form is 114/100 units. Read it as one hundred and fourteen hundredths.
| Description | Counted in hundredths |
|---|---|
| 1 unit | 100 hundredths |
| 3 tenths | 30 hundredths |
| 1 unit and 3 tenths | 130 hundredths |
| 9 tenths and 9 hundredths | 99 hundredths |
There can be more than nine tenths or more than ninety-nine hundredths in an ungrouped quantity. For instance, 130 hundredths is perfectly meaningful. Grouping it gives 1 unit and 30 hundredths, or 1 unit and 3 tenths. In later notation, the places will record this grouped form.
Locating and Comparing Hundredths
Between two consecutive tenth divisions, place ten equal smaller intervals. The first small interval after a tenth division adds one hundredth, the second adds two hundredths, and so on. When counting an endpoint, begin at the labelled starting value rather than treating every scale as if it begins at zero.
The labels 1.10, 1.14, and 1.20 are a preview of decimal notation. Here they stand for 1 + 10/100, 1 + 14/100, and 1 + 20/100 units. Their written form will be explained fully in Decimal Place Value.
Problem
Which is longest and which is shortest: 45/100, 54/100, 5/10, and 4/10 units?
- 1.Convert tenths to hundredths: 5/10 = 50/100 and 4/10 = 40/100.
- 2.Compare the counts 45, 54, 50, and 40.
- 3.The longest is 54/100 unit and the shortest is 4/10 unit.
- 4.In increasing order: 4/10 < 45/100 < 5/10 < 54/100.
Problem
Compare 3 + 6/10, 3 + 6/100, and 3 + 6/10 + 6/100 units.
- 1.All three quantities contain 3 whole units, so compare their fractional parts.
- 2.The fractional parts contain 60, 6, and 66 hundredths respectively.
- 3.Therefore 3 + 6/100 < 3 + 6/10 < 3 + 6/10 + 6/100.
- 4.Six tenths is ten times as large as six hundredths because each tenth contains ten hundredths.
Draw a unit strip, divide it into ten equal parts, and subdivide one tenth into ten equal parts. Locate 3/100, 3/10, and 33/100 of the full unit. Explain why these points differ even though their descriptions all contain the digit 3.
The denominator identifies the size of each part. Three hundredths is smaller than three tenths. Comparing only the numerators would miss this difference. First convert the quantities to the same-sized parts.
Check Your Understanding
Use the ideas from this lesson to choose an answer. Explain your choice to yourself before opening the explanations below.
Quiz
How many hundredths make one tenth?
How many hundredths are in 4 units and 45 hundredths?
Which equals 1 + 1/10 + 4/100?
Which is largest?
Why does subdividing each tenth into ten parts produce hundredths?
One tenth contains ten hundredths.
Practice Problems
- Write 2 + 7/10 + 8/100 units entirely in hundredths.
- Write 537 hundredths as whole units, tenths, and hundredths.
- Arrange 7 + 3/10 + 5/100, 7 + 5/10, and 7 + 41/100 in increasing order.
- Which is longer: 8/10 + 2/100 units or 1 + 8/100 units? Explain.
- A unit interval is divided into one hundred equal parts. What length is reached after the ninety-ninth part? How much remains to the next unit?
- Explain why 1 + 3/10 units and 130/100 units identify the same point on a scale.
Two units give 200 hundredths, seven tenths give 70, and the remaining part gives 8. Total = 278/100 units.
Key Takeaways
• A hundredth is one of one hundred equal parts of a unit. • Dividing each tenth into ten equal parts produces hundredths. • Ten hundredths make one tenth. • One hundred hundredths make one whole unit. • Different groupings can describe the same measurement. • Compare fractional lengths using equal-sized parts.