Cut every tenth into ten
0.3 is three tenths: a bar cut into 10 equal parts, with 3 of them colored.
Now cut every tenth into ten smaller pieces. The bar has 10 × 10 = 100 pieces, and each one is a hundredth of the whole bar. The 3 colored tenths hold 3 × 10 = 30 of the little pieces, so 0.3 is 30 hundredths.
0.3 is 3 of the 10 equal parts.
Every tenth is cut into ten. The same colored part is now 30 of the 100 pieces.
The second place after the point
Hundredths are written in the second place after the decimal point. 30 hundredths is 0.30: 3 in the tenths place and 0 in the hundredths place. 0.30 and 0.3 are the same amount, counted in smaller pieces.
Each place after the point is worth a tenth of the place to its left, just as a one is a tenth of a ten. So 0.47 is 4 tenths and 7 hundredths. Read the digits without the point and name the last place: 0.47 is 47 hundredths, or .
A square cut into 100 equal parts, with 47 of them shaded: 4 full rows of ten, which are 4 tenths, and 7 more hundredths.
Hundredths on a number line
On a number line from 0 to 1, the tenths are 0.1, 0.2, 0.3 and so on. Cut the space from 0.2 to 0.3 into ten equal steps, and each step is a hundredth: 0.21, 0.22, 0.23, up to 0.29. The number 0.27 is 7 hundredths past 0.2.
the tenth from 0.2 to 0.3 holds ten hundredths, and every number inside it is < 0.3, however large its last digit looks: 0.25 = 25/100 < 30/100
Find 0.27 between 0.2 and 0.3
The tenth from 0.2 to 0.3 is drawn again underneath, cut into ten hundredths. Move the marker along it to 0.27.
Two places, no more and no fewer
is 0.47, and the two digits fill the two places after the point. Writing 0.047 moves the digits one place too far to the right: that is 47 thousandths, ten times too small. Writing 47.0 turns them into 47 wholes, but is less than one whole, so a 0 goes before the point.
A zero can hold a place open. 7 hundredths is 0.07: the 0 in the tenths place keeps the 7 in the hundredths place. 0.7 would be 7 tenths, which is 70 hundredths.
Worked example: Reading a Height Chart Marked in Hundredths
Question A height chart on a wall is marked in meters. Its long lines are labeled 1.2, 1.3 and 1.4. Between each pair of long lines there are nine short lines, which divide the space into ten equal parts. In January, the top of Mei's head reached the 7th short line above 1.2. In July of the next year, eighteen months later, it reached the 5th short line above 1.3. (a) What was Mei's height at each reading? (b) How many centimeters did Mei grow in those eighteen months?
1.The ten equal parts between two long lines split one tenth of a meter into ten, so each short line marks one hundredth of a meter, 0.01 m.
Nine short lines cut each tenth into ten equal parts, so each short line is one hundredth of a meter. 2.January's mark is 7 hundredths above 1.2: 1.2 + 0.07 = 1.27 m. July's mark is 5 hundredths above 1.3: 1.3 + 0.05 = 1.35 m.
January: 1.2 + 0.07 = 1.27 m. July: 1.3 + 0.05 = 1.35 m. 3.(a) Mei was 1.27 m tall in January and 1.35 m tall in July.
(a) 1.27 m in January and 1.35 m in July. 4.Count up the scale from 1.27: 3 hundredths reach 1.3, and 5 more reach 1.35. That is 3 + 5 = 8 hundredths of a meter.
3 hundredths up to 1.3, then 5 more: 8 hundredths of a meter. 5.(b) One hundredth of a meter is 1 cm, so Mei grew 8 cm. Check: 1.35 − 1.27 = 0.08 m, which is 8 cm.
(b) One hundredth of a meter is 1 cm, so Mei grew 8 cm.
Answer: (a) January 1.27 m, July 1.35 m; (b) 8 cm
Common mistakes
- Reading the 7th short line above 1.2 as 1.9 by counting each short line as a tenth. The long lines mark the tenths, and a short line marks one tenth of a tenth, which is a hundredth.
- Giving the growth as 0.08 cm. The subtraction gives 0.08 m, and each hundredth of a meter is one centimeter, so the growth is 8 cm.