Reading Decimal Places

Activities to try

1. 1

   Reveal each digit's value (digit × place-unit)

   Why it works: A digit's worth is its face value times the unit of the column it sits in; adjacent decimal places differ by a factor of ten, not by addition, so the same digit can mean very different amounts.

   1. Write or display a number to three decimal places, e.g. 4.378, above a place-value chart with columns labelled Ones . tenths hundredths thousandths and units 1, 1/10, 1/100, 1/1000.
   2. For each digit, say and write its value as digit × place-unit: the 7 is 7 × 1/100 = 7 hundredths = 0.07; the 8 is 8 × 1/1000 = 8 thousandths = 0.008.
   3. State explicitly how adjacent places relate: the hundredths place is one tenth of the tenths place (÷10 moving right, ×10 moving left).
   4. Within a single number containing two identical digits in adjacent decimal columns, e.g. 2.335 (2 ones, 3 tenths, 3 hundredths, 5 thousandths), compare the two 3s and explain why their values differ (3 tenths = 0.3 versus 3 hundredths = 0.03) even though the digit is the same.
2. 2

   Reverse build: reconstruct the numeral from given values (placeholder zeros)

   Why it works: A placeholder zero is worth 0 itself, but it does real work by holding a column open; omitting a zero that comes before other digits shifts every later digit into the wrong place and produces a different number. Reconstruction proves flexible, two-way understanding of place value.

   1. Given a set of digit-values — 4 ones, 0 tenths, 7 hundredths, 3 thousandths — place each into its column on a place-value chart and read off the numeral.
   2. Write the resulting number: 4.073.
   3. Deliberately try leaving the empty tenths column blank and read what you get: 4.73. Compare 4.073 with 4.73 and explain why they are different numbers.
   4. Repeat with another set that includes a zero in a middle place (e.g. 3 ones, 0 tenths, 0 hundredths, 5 thousandths = 3.005) and justify each zero's job.
3. 3

   Which is worth more — the smaller digit or the larger?

   Why it works: Place, not face value, determines worth in a decimal: reasoning about the column must override the surface impression that the bigger digit is worth more or that a digit further right is larger.

   1. Compare the value of the 3 and the 7 in 4.378: state the 3 is 3 tenths (0.3) and the 7 is 7 hundredths (0.07).
   2. Decide which is worth more and justify it — the 3, because tenths are ten times bigger chunks than hundredths, so 3 tenths outweighs 7 hundredths even though 7 is the larger digit.
   3. Mark 0.3 and 0.07 on a 0–1 number line to see that 3 tenths is a bigger portion than 7 hundredths.
   4. Discuss: when 4.378 becomes 4.387, whose value changed — the 7's or the 8's? Explain using the columns: both changed, since the 7 and 8 swapped between the hundredths and thousandths places.