4.H.1 — Tenths and hundredths as fractions.
Step 01 of 04
Tenths = parts when a whole is split into 10 equal pieces. Hundredths = parts when split into 100.
1 tenth=101,1 hundredth=1001
Step 02 of 04
Mixed example. 3 tenths + 4 hundredths = how many hundredths?
Convert tenths to hundredths: 3 tenths = 30 hundredths. So total = 34 hundredths = 34/100.
103+1004=10030+1004=10034
Step 03 of 04
Visualize on a 10×10 grid. The whole grid = 1. Each row = 1/10. Each small square = 1/100. Shading 34 small squares = 34/100 = 0.34.
Step 04 of 04
Equivalent forms.
| 7 tenths | →= 7/10=70/100 |
| 25 hundredths | →= 25/100=1/4 |
| 100 hundredths | →= 100/100=1 (whole) |
Key insight
Tenths split a whole into 10. Hundredths into 100. Each tenth = 10 hundredths. Use a 10×10 grid to visualize hundredths.
4.H.2 — Decimal notation for fractions.
Step 01 of 04
The decimal point separates whole numbers from FRACTIONAL parts. The first place after is tenths, the second is hundredths.
| 0.1 | →=1/10 (one tenth) |
| 0.01 | →=1/100 (one hundredth) |
| 0.7 | →=7/10 |
| 0.34 | →=34/100 |
Step 02 of 04
Convert fraction → decimal.
106=0.610043=0.43
Number of digits after the decimal point matches the number of zeros in the denominator: tenths (1 digit), hundredths (2 digits).
Step 03 of 04
Convert decimal → fraction.
0.5=105=21
0.75=10075=43
Read the decimal: "seventy-five hundredths." That literally tells you the fraction.
Step 04 of 04
Mixed numbers as decimals.
3102=3.2
510067=5.67
The whole-number part stays to the LEFT of the decimal point.
Key insight
First place after the decimal = tenths, second = hundredths. To convert a fraction with denominator 10 or 100, just place the digits in those positions.
4.H.3 — Compare decimals to hundredths.
Step 01 of 04
Compare decimals digit by digit, place by place, starting from the LEFT (highest value).
First, line up the decimal points. Pad shorter decimals with zeros at the right so they have the same number of decimal places.
Step 02 of 04
Worked example. Compare 0.7 and 0.65.
Pad: 0.7 = 0.70 (same as 0.7, just makes comparison easier). Compare tenths: 7 vs. 6 — 7 is bigger.
0.70>0.65
Don't be fooled: 0.7 is NOT smaller just because it has fewer digits. The leading 0.7 means 7 tenths, which is bigger than 6 tenths.
Step 03 of 04
Same first digit? Move to the next place.
0.43 vs. 0.47. Tenths both 4 — same. Hundredths: 3 vs. 7. 7 wins. So0.47>0.43.
Step 04 of 04
Order three or more decimals. Same idea, just compare left-to-right until you can sort.
Order: 0.5, 0.42, 0.6, 0.55. Pad to: 0.50, 0.42, 0.60, 0.55. Sort by tenths first: 0.42 (tenths 4), then 0.50 / 0.55 (tenths 5), then 0.60. Sub-sort the 5-tenths group by hundredths: 0.50 < 0.55. Final: 0.42 < 0.50 < 0.55 < 0.60.
Key insight
Pad with zeros so all decimals have the same number of decimal places. Compare digit by digit, starting from the left. Same digit → check the next place.