Decimals are a place-value system that continues past the ones place. The first place to the right names tenths; the next names hundredths; then thousandths. Writing 0.35 means three tenths and five hundredths, not thirty-five ones. The decimal point marks a boundary between different unit sizes.
MATH-103 · MODULE 04
Decimals: Place Value and Calculation
Read decimals as base-ten fractions, operate with aligned units, and estimate before trusting a result.
A rational number toolkit
Make the relationship visible before the procedure tries to hide it.
This course begins every module with a teaching conversation and treats fractions, decimals, percents, and ratios as connected ways to describe quantity. Work one decision at a time, choose a representation that fits, then check whether the result belongs in a sensible range.
Restoring this module…
Before you begin
Decimal places name units. Read the units before lining up digits.
For comparison and calculation, make the units line up. Zeros can be added as placeholders without changing the value, so 0.7 and 0.70 are the same amount. An estimate using nearby tenths or whole numbers tells you whether the exact answer belongs in a believable range.
This route connects a place-value chart, a number line, and an equation. Move deliberately among them. When a calculation feels like a string of symbols, return to the chart and say the unit of each digit aloud.
Start
Read the place, then read the amount
Learning target
A digit's value depends on its place: tenths, hundredths, and thousandths are different-sized units.
Decimals extend place value to the right of the ones place. In 2.405, the 4 names tenths, the 0 names hundredths, and the 5 names thousandths.
Read or listen to the teaching conversation for this step
Module 4, Start
Transcript: Do not treat the digits after a decimal as a whole number. Each position names a smaller base-ten unit. Read the place name before you decide the value.
Guided practice
Make one decision, get a useful response, then continue.
A response counts as independently complete only when it is correct. Hints and recovery routes remain available whenever you need them.
Name a decimal place
In 6.307, what value does the 3 represent?