Fractions, Decimals, and Their Operations
Decimals to hundredths are the natural extension of the place value system to the right of the ones position. Tenths are like the tens of the decimal world: 0.4 is four tenths, or 4/10. Hundredths are like ones: 0.07 is seven hundredths, or 7/100. The connection between fractions and decimals is not a coincidence: decimals ARE fractions with denominators that are powers of 10. Students who understand this connection can move fluidly between the two representations.
Decimals as place value extensions
The decimal point separates the whole number part from the fractional part. Tenths: 0.4 = 4/10. Hundredths: 0.07 = 7/100. So 0.47 = 4/10 + 7/100 = 40/100 + 7/100 = 47/100. Base-ten blocks: if the hundreds flat = 1, then one rod = 0.1 (one tenth), and one small cube = 0.01 (one hundredth). The same blocks, different unit assignment, same proportional relationships.
Ordering fractions with benchmarks
Is 3/8 closer to 0, 1/2, or 1? 3/8 is just under 4/8 = 1/2, so closer to 1/2. Is 5/6 closer to 1/2 or 1? 5/6 is close to 6/6 = 1, so closer to 1. Fraction benchmarks eliminate the need to convert to common denominators for rough comparisons, building intuitive fraction sense that supports estimation.
Money as a decimal context
$4.37 = 4 dollars, 3 dimes, 7 pennies = 4 + 3/10 + 7/100. Every dollar amount is a decimal to hundredths. Students who have been handling money since Kindergarten have been working with decimals without knowing it. Making this connection explicit gives decimal notation immediate, lived meaning.