Math // Fractions

Decimals for Tenths & Hundredths

Use decimal notation for fractions with denominators 10 or 100; read and write decimal numbers as fractions (e.g. 0.62 = 62/100, 0.71 = 71/100)

Ages
9 to 10
Type
Method
Builds on
3 topics
Leads to
3 topics
Standards
2 codes

Quick check

If the learner sees a price tag showing £0.65, can they rewrite it as a fraction — and go the other way, turning 47/100 into a decimal?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Rewrite 0.62 as 62/100
  • Write 3/10 as 0.3 and locate on a number line
  • Read 0.07 and express as 7/100

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

3 topics

You are here

Decimals for Tenths & Hundredths

Ages 9 to 10 // Method

Leads to

3 topics
  • Tenths (age 9+)Required

    Fractions // Ages 9 to 10

    Decimal notation for 10ths/100ths is prerequisite to extending to thousandths

  • Understanding PercentagesRequired

    Fractions // Ages 9 to 10

    Decimal notation for fractions is prerequisite to understanding % as parts per 100

  • Fractions on a number lineHelpful

    Measurement // Ages 9 to 10

    Decimal notation supports measurement problems with decimals

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

Learners move fluently in BOTH directions between decimal notation and tenths/hundredths fractions: read 0.62 as 62/100, write 3/10 as 0.3, read 0.07 as 7/100, and locate these on a 0–1 number line. The skill rests on place-value meaning — the first place after the point is tenths, the second is hundredths — so the denominator is read from the final place (10 → one place, 100 → two places), and a placeholder zero is needed when the numerator has fewer digits than the denominator has zeros (7/100 = 0.07). Learning and checking should deliberately use placeholder and single-digit-numerator cases, because a digit-copying rule produces correct answers on easy items but fails exactly there.

Common misconceptions

  • Dropping the placeholder zero: writing 9/100 as 0.9, or reading 0.07 as 7/10.
  • Adding an unneeded zero: writing 3/10 as 0.03 by over-applying 'hundredths = two places'.
  • Using one denominator for every decimal: writing 0.4 as 4/100 regardless of the number of places.
  • Reversing digits or reading position wrong: 0.62 → 6/2 or 26/100.
  • Placing decimals on the number line by whole-number reasoning rather than by tenths/hundredths.

Useful representations

  • Place-value chart (tenths | hundredths) beside the fraction
  • 10×10 hundredths grid shaded to match the decimal and the fraction
  • Number line for locating 0.3, 0.4, 0.62
  • Contrasting sets {3/10, 3/100} and {0.7, 0.07} to drill the placeholder
  • Bidirectional conversion cards (decimal on one side, fraction on the other)

Teaching practices

  • Practise BOTH directions from the start (decimal→fraction and fraction→decimal) using a place-value chart so the child reads the denominator off the final place.
  • Foreground the placeholder: pair 3/10 = 0.3 with 7/100 = 0.07 and 3/100 = 0.03 so the child learns that hundredths always occupy two places and a zero holds an empty tenths place.
  • Link every conversion to a picture — a hundredths grid and a number-line location — so the symbolic answer is checked against a quantity, catching reversals like 0.62 → 6/2.
  • Use ragged and single-digit-numerator cases deliberately (0.4, 0.07, 9/100) because these are where the placeholder rule bites and hollow digit-copying fails.
  • Have the child read the decimal aloud in place-value language ('sixty-two hundredths') before writing the fraction, so the denominator is heard.

Activities to try

  1. 1

    Two-way converter checked against a grid and a number line

    Why it works: The placeholder zero is not a rule to memorise but something you can see: for 9/100 the zero keeps the nine out of the tenths place. The denominator is determined by the final decimal place, and every symbolic answer can be checked against a shaded quantity and a position on the line.

    1. Enter a decimal (e.g. 0.62) and write the matching fraction; confirm against a 10×10 hundredths grid that shades 62 squares and a number-line marker that lands just past halfway.
    2. Enter a fraction (e.g. 3/10) and write the matching decimal (0.3); confirm by shading 3 of the ten columns and placing the point on the line.
    3. Do the hard placeholder case: for 9/100, if you write 0.9 the grid floods with ninety squares — far more than nine — so the mismatch is obvious; correct it to 0.09 so exactly nine squares glow.
    4. Run rapid two-way rounds (decimal→fraction and fraction→decimal) across a deliberate set of placeholder and ragged cases: 0.07, 9/100, 0.4, 3/100.
    5. Read each decimal aloud in place-value language ('sixty-two hundredths', 'seven hundredths') before writing the fraction, so the denominator is heard.
  2. 2

    Contrast sets that drill the placeholder

    Why it works: Tenths and hundredths of the same digit look similar in writing but differ ten-fold in size; the number of decimal places and the presence of a placeholder zero both follow from which place the final digit occupies.

    1. Work matched pairs side by side: {3/10, 3/100} and {0.7, 0.07}, writing each as both a fraction and a decimal.
    2. For each pair, shade a hundredths grid for both members so the size difference is visible (3 columns vs 3 squares; 70 squares vs 7 squares).
    3. State in words why one needs a placeholder zero and the other does not.
    4. Sort a mixed set of cards (decimal on one side, fraction on the other) and self-check by flipping, giving special attention to 0.4, 0.07 and 9/100.
  3. 3

    Annotated place-value chart as a reference (scaffold)

    Why it works: A worked reference makes the place–denominator link and the placeholder rule explicit, but fluency comes from doing many items, not from reading examples.

    1. Study a place-value chart (tenths | hundredths) beside a couple of worked conversions, e.g. 0.62 = 62/100 and 9/100 = 0.09.
    2. Read a short explanation of why the placeholder zero appears in 0.09 but not in 0.3.
    3. Return to the converter or contrast-set tasks and reproduce the method on new values without looking.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
Common Core State Standards for Mathematics
4.NF.6
The national curriculum in England: Key stages 1 and 2 framework document
Ma5/2.4f

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