Math // Fractions

Decimal equivalents of tenths and hundredths

Recognise and write decimal equivalents of any number of tenths or hundredths (e.g. 3/10 = 0.3, 27/100 = 0.27)

Ages
8 to 9
Type
Concept
Builds on
2 topics
Leads to
7 topics
Standards
1 code

Quick check

If the learner sees 7/10 on a price label, can they rewrite it as a decimal — and do the same thing for 43/100?

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.
  • Write 7/10 as 0.7 and vice versa
  • Convert 45/100 to 0.45
  • Place 0.3 and 3/10 at the same point on a number line

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

2 topics
  • Tenths (age 8+)Required

    Fractions // Ages 8 to 9

    Must understand hundredths before writing decimal equivalents

  • Decimal & Percent NotationRequired

    Fractions // Ages 8 to 11

    Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary

You are here

Decimal equivalents of tenths and hundredths

Ages 8 to 9 // Concept

Leads to

7 topics
  • Fraction-Decimal EquivalentsRequired

    Fractions // Ages 8 to 9

    General decimal equivalents prerequisite to specific 1/4, 1/2, 3/4 equivalents

  • Decimal place value (age 8+)Required

    Fractions // Ages 8 to 9

    Must understand decimal notation to compare decimals

  • Dividing by 10 and 100Required

    Fractions // Ages 8 to 9

    Must know decimal notation to express results of dividing by 10/100

  • Decimals and fractionsRequired

    Fractions // Ages 8 to 9

    Must understand decimal notation for measure/money problems

  • Decimal place valueRequired

    Fractions // Ages 8 to 9

    Must understand decimal notation to round decimals

  • Decimals for Tenths & HundredthsRequired

    Fractions // Ages 9 to 10

    Y4 decimal equivalents of 10ths/100ths is prerequisite to formal decimal notation for fractions

  • Fractions on a number lineHelpful

    Mathematical Thinking // Ages 8 to 9

    Decimal equivalents exercise fluency between fraction and decimal representations

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

A decimal with one or two decimal places is another name for a fraction with denominator 10 or 100: the same quantity, the same point on the number line (3/10 = 0.3, 27/100 = 0.27). The load-bearing insight is that the PLACE, not just the digits, carries the denominator: the first place after the point counts tenths, the second counts hundredths, so 7 hundredths needs a placeholder zero (0.07), not 0.7. Teach the two forms as interchangeable labels for one amount by tying each decimal to its fraction and to a single point on a line or a shaded grid, so children do not treat 0.3 and 3/10 as different things.

Common misconceptions

  • Dropping the placeholder zero — writing 7/100 as 0.7 (or reading 0.07 as 7/10), ignoring that the place fixes the denominator.
  • Treating a decimal and its fraction as different numbers — not seeing 0.3 and 3/10 as the same quantity at the same point.
  • Reading the digits after the point as an ordinary whole number ('0.27 means twenty-seven') rather than as 27 hundredths.
  • Mapping the numerator straight after the point regardless of denominator, so 3/10 and 3/100 both become 0.3.
  • Thinking annexing a zero changes the value (0.3 vs 0.30 seen as different).

Useful representations

  • 10×10 hundredths grid shaded and labelled with both the fraction and the decimal
  • Place-value chart with tenths and hundredths columns beside the fraction
  • Number line where 0.3, 0.30 and 3/10 mark the same point
  • Contrasting pairs 3/10 = 0.3 vs 3/100 = 0.03 to spotlight the placeholder zero
  • Bidirectional fraction↔decimal cards for matching

Teaching practices

  • Introduce the decimal as a re-labelling of a tenths/hundredths fraction on the SAME grid or number line — shade 27 of 100 squares and write both 27/100 and 0.27 for the identical picture.
  • Make the place-value columns explicit: the first place after the point is tenths, the second is hundredths, so the denominator is read off the position; write fractions and decimals side by side in a place-value chart.
  • Stress the placeholder zero with contrasting pairs — 3/10 = 0.3 but 3/100 = 0.03, and 7/100 = 0.07 not 0.7 — so children attend to place, not just to the digits.
  • Place 0.3 and 3/10 (and 0.30) at the same point on a number line to establish that the two notations name one quantity, defeating 'a decimal and a fraction are different numbers'.
  • Read decimals in place-value language ('twenty-seven hundredths', 'three tenths') not as 'point two seven', so the fraction meaning stays audible.

Activities to try

  1. 1

    Shade, name it twice, and pin one point

    Why it works: A decimal and its fraction are one number wearing two names; the place after the point fixes the denominator, so the placeholder zero in 0.07 holds the tenths place empty and is not decoration.

    1. On a 10×10 hundredths grid, shade 27 of the 100 squares; write the fraction (27/100) and the decimal (0.27) for the exact same picture, side by side in a place-value chart with tenths and hundredths columns.
    2. Mark where this amount sits on a 0-to-1 number line; confirm 27/100 and 0.27 land on the same single point.
    3. Now shade just 7 squares. Write the fraction (7/100) and decide the decimal. Predict and then check: does it write as 0.7 or 0.07?
    4. Compare where 0.7 would fall on the number line versus where your 7 shaded squares sit — notice 0.7 lands far past 7 hundredths, exactly at seven tenths.
    5. Toggle between 0.3, 0.30 and 3/10 and place each on the number line to confirm all three mark the identical point.
  2. 2

    Predict then reconcile on the number line

    Why it works: Committing to a prediction and its reason surfaces whether a child believes a decimal and a fraction are different kinds of number; reconciling with the shared point corrects it.

    1. Before locating anything, predict: will 0.3 and 3/10 land at the same point on a number line, at different points, or is one bigger — and WHY?
    2. State your reason aloud or in writing, then place 0.3, 3/10 and 0.30 on a marked line.
    3. Observe that all three coincide; explain how this fits (or revises) your prediction.
    4. Answer a challenge: a friend says 3/10 and 3/100 both write as 0.3 — what would you tell them, and what should 3/100 actually be?
  3. 3

    Reference grid with reveal flaps

    Why it works: The equivalence of the two notations and the role of the placeholder zero can be seen at a glance as a reference, reinforcing what was built through shading and prediction.

    1. Use a static hundredths grid annotated with both notations: tap or lift a flap on a shaded region to reveal 'this shading is 27/100 = 0.27'.
    2. Open a contrasting-pair flap that shows 3/10 = 0.3 beside 3/100 = 0.03, and a 'why the zero in 0.07?' flap.
    3. Consult a number line showing 0.3 = 3/10 sharing one point.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
The national curriculum in England: Key stages 1 and 2 framework document
Ma/KS2/Y4/F/5

Math // Fractions

More in Fractions

All 67 topics